Class 10 - Arihant - All in one (Math) - ProbabilityContact Number: 9667591930 / 8527521718

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1.

Two coins are tossed simultaneously. Find the probability of getting

(i) exactly two head (ii) atleast one head

2.

Suppose we throw a die once.

(i) What is the probability of getting a number greater than 4?

(ii) What is the probability of getting a number less than of equal to 4?

3.

Two dice are thrown simultaneously. Find the probability of getting a multiple of 2 on one die and a multiple of 3 on the other die.

4.

The king, queen and jack of spades are removed from a deck of 52 playing cards and then well-shuffled. One card is selected from the remaining cards. Find the probability of getting

(i) a spade (ii) a king

5.

Three bags containing 10 orange, 10 green and 10 red balls, respectively are mixed together in one large bag. If one of the balls is taken out at random without looking into the bag, then what is the probability that it is

(i) orange (ii) not orange

6.

Cards numbered 1, 2, 3, 4, 5,...,17 are put in a box and mixed thoroughly. One person draws a card from the box. Find the probability that the number on the card is

(i) an odd number (ii) a prime number

(iii) divisible by 3 (iv) divisible by 2 and 3 both

(v) a multiple of 3 or 5

7.

A missing helicopter is reported to have crashed somewhere in the rectangular region shown in figure. What is the probability that it crashed inside the lake shown in the figure?

8.

A lot consists of 48 mobile phones of which 42 are good, 3 have only minor defect and 3 have major defect. Varnika will buy a phone, if it is good but the trader will only buy a mobile, if it has no major defect. one phone is selected at random from the lot. What is the probability that it is

(i) acceptable to Varnika?

(ii) acceptable to the trader?

9.

Savita and Hamida are friends. What is the probability that both will have

(i) the same birthday? (ignoring a leap year)

(ii) different birthdays?

10.

In a musical chair game, the person playing the music has been advised to stop playing the music at any time within 2 min after she starts playing. What is the probability that the music will stop within the first half-minute after starting ?

11.

Two players Neha and Shivani play a tennis match. It is known that the probability of Neha winning the match is 0.62. What is the probability of Shivani winning the match?

12.

Complete the following statements

(i) Probability of an event E + Probability of the event 'not E' = ............

(ii) The probability of an event that cannot happen is ......... such an event is called...........

(iii) The probability of an event that is certain to happen is ........ such an event is called .........

(iv) The sum of the probabilities of all the element events of an experiment is ........

(v) The probability of an event is greater than or equal to .......... and less than or equal to ..........

13.

Which of the following experiments have equally likely outcomes? Explain.

(i) A driver attempts to start a car. The car starts or does not start.

(ii) A player attempts to shoot a basketball. She/He shoots or misses the shot.

(iii) A trial is made to answer a true-false question. The answer is right or wrong.

(iv) A baby is born. It is a boy or a girl.

14.

Why is tossing a coin considered to be a fair way of deciding which team should get the ball at the beginning of a football game?

15.

Which of the following cannot be the probability of an event ?

(1) $\frac{2}{3}$ (2) - 1.5 (3) 15% (4) 0.7

16.

If P(E) = 0.05, what is the probability of 'not E' ?

17.

A bag contains lemon flavoured candies only. Malini takes out one candy without looking into the bag. What is the probability that she takes out

(i) an orange flavoured candy?

(ii) a lemon flavoured candy?

18.

A piggy bank contains hundred 50 paise coins, fifty Rs 1 coins, twenty Rs 2 coins and ten Rs 5 coins. If it is equally likely that one of the coins will fall out when the bank is turned upside down, then what is the probability that the coin

(i) will be a 50 paise coin?

(ii) will not be a Rs 5 coin?

19.

Gopi buys a fish from a shop for her aquarium. The shopkeeper takes out one fish at random from a tank containig 5 male fishes and 8 female fishes (see figure). What is the probability that the fish taken out is a male fish?

20.

A game of chance consists of spinning an arrow which comes to rest pointing at one of the numbers 1, 2, 3, 4, 5, 6, 7 and 8 (see figure) and these are equally likely outcomes. What is the probability that it will point at

(i) 8?

(ii) an odd number?

(iii) a number greater than 2?

(iv) a number less than 9?

21.

A die is thrown once. Find the probability of getting

(i) a prime number

(ii) a number lying between 2 and 6

22.

One card is drawn from a well-shuffled deck of 52 cards. Find the probability of getting

(i) a king of red colour

(ii) a face card

(iii) a red face card

(iv) the jack of hear

(v) a spade

(vi) the queen of diamond

23.

Five cards-the ten, jack, queen, king and ace of diamonds are well-shuffled with their face downwards. one card is then picked up at random.

(i) What is the probability that the card is the queen?

(ii) If the queen is drawn and put a side, what is the probability that the second card picked up is

(a) an ace? (b) a queen?

24.

12 defective pens arae accidentally mixed with 132 good ones. It is not possible to just look at a pen and tell whether or not it is defective. One pen is taken out at random from this lot. Determine the probability that the pen taken out is a good one.

25.

(i) A lot of 20 bulbs contain 4 defective ones. One bulb is drawn at random from the lot. What is the probability that this bulb is defective?

(ii) Suppose the bulb drawn in (i) is not defective and is not replaced. Now, one bulb is drawn at random from the rest. What is the probability that this bulb is not defective?

26.

A box contains 90 discs, which are numbered from 1 to 90. If one disc is drawn at random from the box, find the probability that it bears

(i) a two-digit number

(ii) a perfect square number

(iii) a number divisible by 5

27.

A child has a die whose six faces show the letters as given below

A B C D E A

The die is thrown once. what is the probability of getting

(i) A? (ii) D?

28.

Suppose, you drop a die at random on the rectangular region shown in figure. What is the probability that it will land inside the circle of diameter 1 m?

29.

A lot consists of 144 ball pens of which 20 are defective and the others are good. Nuri will buy a pen if it is good, but will not buy if it is defective. The shopkeeper draws one pen at random and gives it to her. What is the probability that.

(i) she will but it? (ii) she will not buy it?

30.

Two dice, one blue and one grey, are thrown at the same time. Then

(i) complete the following table:

**Event: Sum on 2 dice ** 2 3 4 5 6 7 8 9 10 11 12

**Probability ** $\frac{1}{36}$ $\frac{5}{36}$ $\frac{1}{36}$

(ii) A student argues that there are 11 possible outcomes 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 and 12. Therefore, each of them has a probability $\frac{1}{11}$. Do you agree with this argument? Justify your answer.

31.

A game consists of tossing a one rupee coin 3 times and noting its outcome each time. Hanif wins, if all the tosses give the same result, i.e. three heads or three tails and losses otherwise. Calculate the probability that Hanif will lose the game.

32.

A die is thrown twice. What is the probability that

(i) 5 will come up atleast once?

(ii) 5 will not come up either time?

33.

Which of the following arguments are correct and which are not correct? Give reason for your answer.

(i) If two coins are tossed simultaneously, there are three possible outcomes - two heads, two tails or one of each. Therefore, for each of these outcomes, the probability is $\frac{1}{3}$.

(ii) If a die is thrown, there are two possible outcomes-an odd number of an even number. Therefore, the probability of getting an odd number is $\frac{1}{2}$.

34.

Two customers, Shyam and Ekta are visiting a particular shop in the same week (Tuesday to Saturday). Each is equally likely to visit the shop on any day as on another day.

What is the probability that both will visit the shop on

(i) the same day?

(ii) consecutive days?

(iii) different days?

35.

A die is numbered in such a way that its faces show the numbers 1, 2, 2, 3, 3, 6. It is thrown two times and the total score in two throws is noted. Completed the following table, which gives a few values of the total score on the two throws

What is probability that the total score is

(i) even?

(ii) 6?

(iii) atleast 6?

36.

A bag contains 5 red balls and some blue balls. If the probability of drawing a blue ball is double that of a red ball determine the number of blue balls in the bag.

37.

A box contains 12 balls, out of which x are black. If one ball is drawn at random from the box, what is the probability that it will be a black ball?

If 6 more black balls are put in the box, the probability of drawing a black ball is now double of what it was before. Find the value of x.

38.

A jar contains 24 marbles, some are green and others are blue. If a marble is drawn at random from the jar, the probability that it is green, is $\frac{2}{3}$. Find the number of blue marbles in the jar.

39.

Find the sum of probabilities of all the elementary events of an experiment.

40.

What is the probabililty of non-occurrence of an event that is certain to happens?

41.

The probability that it will rain today is 0.07. What is the probability that it will not rain today?

42.

In a simultaneous toss of two coins, find the probability of exactly one head.

43.

A die is thrown once. Find the probability of getting an even number less than 5.

44.

If a die is thrown, what is the probability of getting a number less than 3 and greater than 2 ?

45.

Cards marked with numbers 5 to 75 are placed in a box and mixed thoroughly. One card is drawn from the box. Find the probability that the number on the card is oddd.

46.

A number is chosen from 1 to 100. Find the probability that it is a prime number.

47.

A die is thrown once. Find the probability of getting a number which is not a factor of 36.

48.

The probability of getting a rotten egg from a lot of 400 eggs is 0.035. Find the number of rotten eggs in the lot.

49.

A single letter is selected at random from the word 'PROBABILITY'. Find the probabililty that it is a vowel.

50.

A letter of English alphabet is chosen at random. Determine the probability that the letter is a consonant.

51.

A letter is chosen at random from the English alphabet. What is the probability that it is a letter of the word 'RAMANUJAN'?

52.

Find the probability that a non-leap year selected at random will contains 53 Sundays.

53.

A school has five houses A, B, C, D and E. A class has 23 students, 4 from house A, 8 from house B, 5 from hourse C, 2 from house D and rest from house E. A single students is seclected at random to be the class monitor. Find the probability that the selected students is not from A, B and C.

54.

The probability of guessing the correct answer to certain question is p/12. If the probability of not guessing the correct answer to same question is 3/4, then find the value of p.

55.

A girl calculates that the probability of her winning the first prize in a lottery is 0.08. If 6000 tickets are sold then how many tickets has she bought?

56.

A number x is chosen at random from the number -4, -3, -2, -1, 0, 1, 2, 3, 4.

What is the probability that $\left|x\right|$ < 2?

57.

A card is drawn from a well-shuffled pack of 52 cards. Find the probability that the card drawn is neither a red card nor a queen.

58.

A bag contains 2 green, 3 red and 4 black balls. A ball is taken out of the bag at random. Find the probability that the selected ball is

(i) not green (ii) not black

59.

From a group of 2 boys and 2 girls, two children are selected at random. List the possible outcomes. Find the probability that one boy and one girl are selected.

60.

Two friends were born in the year 2000. What is the probability that they have the same birthday?

61.

Apoorv throws two dice once and computes the product of the numbers appearing on the dice. Peehu throws one die and squares the number that appears on it. Who has the better chance of getting the number 36? why?

62.

An integer is chosen between 0 and 100. What is the probability that it is

(i) divisible by 7?

(ii) not divisible by 7?

63.

Box A contains 25 slips of which 19 are marked Rs 1 and other are marked Rs 5. Box B contains 50 slips of which 45 are marked Rs 1 and others are marked Rs 13. Slips of both boxes are put into a third box and reshuffled. A slip is drawn at random. What is the probability that it is marked other than Rs 1?

64.

A number is selected at random from first 50 natural numbers. Find the probability that it is a multiple of 3 and 4.

65.

A number is selected from the numbers 2, 3, 3, 5, 5, 5, 7, 7, 7, 7, 9, 9, 9, 9, 9 at random. Find the probability that the number selected is

(i) their median

(ii) their mode

66.

67.

Two dice are thrown at the same time and the product of numbers appearing on them is noted. Find the probability that the product is less than 9.

68.

There are 100 cards in a bag on which numbers from 1 to 100 are written. A card is taken out from the bag at random. Find the probability that the number on the selected card

(i) is divisible by 9 and is a perfect

(ii) is a prime number greater than 80

69.

A square of side 5 cm is drawn in the interior of another square of side 10 cm and shaded as shown in the following figure. A point is selected at random from the interior of square ABCD. What is the probability that the point will be chosen from the shaded part?

70.

Two dice are thrown simultaneously. What is the probability that the sum of the numbers appearing on the dice, is

(i) 7?

(ii) not a prime number?

(iii) 1?

71.

In a game, the entry fee is Rs 5. The game consists of tossing a coin 3 times. If one or two heads show, Sweta gets her entry fee back. If she tosses 3 heads, she receives double the entry fee. Otherwise, she will loss. For tossing a coin three times, find the probability that she

(i) losses the entry fee

(ii) gets double entry fee

(iii) just gets her entry fee

72.

A game of chance consists of an arrow which comes to rest pointing at one of the regions 1, 2 or 3. O is the centre of the circle, OC$\perp $AB.

Find the probability that

(i) arrow is resting on 3

(ii) arrow is resting on 1

(iii) arrow is not resting on 2

73.

Cards with numbers 2 to 101 are placed in a box. A card is selected at random. Find the probability that the card has

(i) an even number

(ii) a square number

74.

Two dice are thrown together. Find the probability that the product of the numbers on the top of the dice is

(i) 6 (ii) 12 (iii) 7

75.

One card is drawn from a pack of 52 cards, each of the 52 cards being equally likely to be drawn. Find the probability that the card drawn is

(i) a red king

(ii) '2' of spade

(iii) '10' of a black suit

76.

A pair of dice is thrown once. Find the probability of getting

(i) doublet of prime numbers

(ii) a doublet of odd numbers

77.

78.

Three different coins are tossed together. Find the probability of getting

(i) exactly two heads

(ii) atleast two heads

(iii) atleast two tails

79.

80.

A child's game has 8 triangles of which 3 are blue and rest are red and 10 squares of which 6 are blue and rest are red. One piece is lost at random. Find the probability that it is a

(i) triangle (ii) square

(iii) square of blue colour (iv) triangle of red colour

81.

All the three face cards of spades are removed from a well-shuffled pack of 52 cards. A card is drawn at random from the remaining pack. Find the probability of getting

(i) a black face card

(ii) a queen

(iii) a black card

(iv) a spade

82.

A bag contains white, black and red balls only. A ball is drawn at random from the bag. The probability of getting a white ball is $\frac{3}{10}$ and that of a black ball is $\frac{2}{5}$. Find the probability of getting a red ball. If the bag contains 20 black balls, then find the total number of balls in the bag.

83.

There are 1000 sealed envelopes in a box, 10 of them contain a cash prize of Rs 100 each, 100 of them contain a cash prize of Rs 50 each and 200 of them contain a cash prize of Rs 10 each and rest do not contain any cash prize. If they are well-shuffled and an envelope is picked up out, what is the probability that it contains no cash prizes ?

84.

In the given figure, points A, B, C and D are the centres of four circles that each have a radius of length one unit. If a point is selected at random fromt the interior of square ABCD, what is the probability that the point will be chosen from the shaded region ?

85.

A number x is selected at random from the numbers 1, 4, 9, 16 and another number y is selected at random from the numbers 1, 2, 3, 4. Find the probability that the value of xy is more than 16.

86.

A traffic signal displays green light for two minutes to allow passage of traffic on a particular road. If the signal is currently displaying green light, then find the probability that it will turn red within the next half a minute.

87.

A group of students from a school decided to donate blood. The blood group of 16 students of Class X are recorded as follows

A, B, O, O, AB, O, A, O, B, A, O, B, A, O, O, AB

(i) Find the probability of blood group

(a) O (b) A

(ii) What value is depicted from this activity?

88.

A group consists of 12 persons, out of which 3 are extremely patient, other 6 are extremely honest and rest are extremely kind. A person from the group is selected at random. Assuming that each person is equally likely to be selected, find the probability of selecting a person who is

(i) extremely patient

(ii) extremely kind or honest. Which of the above values you prefer more?

89.

Anu, Priya and Jyoti were flighting to get first chance in a game. Anu says, "Let us toss two coins. If both heads appear, Priya will take first chance, if both tails appear, Jyoti will get it and if one head and one tail appears, I will get the chance".

(i) What is the probability of Anu, Priya and Jyoti getting the first chance?

(ii) Is her decision fair?

(iii) What quality of her character is being depicted here?

90.

In a throw of a die, find the probability of getting an odd number less than 6.

91.

A student says that, if you throw a die, it will show up 1 or not 1. Therefore, the probability of getting not 1 each is equal to $\frac{1}{2}$. Is this correct? Give reasons.

92.

In a throw of a pair of dice, what is the probability of getting a doublet or some number?

93.

A box contains 90 discs, numbered from 1 to 90. If one disc is drawn at random from the box, find the probability that it bears a prime number less than 23.

94.

Find the probability that a number selected at random from the number, 1, 2, 3,....., 15 is a multiple of 4

95.

Find the probability of getting a perfect square number from the numbers 1 to 10.

96.

What is the probability of getting exactly two tails, when two coins are tossed together?

97.

If P(E) = 0.15, then find P (Not E).

98.

If 1 toss a coin 3 times and get head each time, then 1 should expect a tail to have a higher chance in the 4th toss. Is it true?

99.

In a family having three children, there may be no girl, one girl two girls or three girls. So, the probability of each is $\frac{1}{4}$. Is it true?

100.

In a family of 3 children, find the probability of having atleast one boy.

101.

In a cricket match a batsman hits the boundary 8 times out of 40 balls he plays. Find the probability that he did not hit the boundary.

102.

A ticket is drawn at random from a bag conaining tickets numbered from 1 to 40. Find the probability that the selected ticket has a number, (i) which is a multiple of 7 (ii) which is a multiple of 5.

103.

Cards marked with numbers 5, 6, 7,....,74 are placed in a bag and mixed thoroughly. One card is drawn at random from the bag. Find the probabillity that the number on the card is a perfect cube.

104.

A bag contains 6 red, 3 black and 6 white balls. A ball is selected at random from the bag. Find the probability that the selected ball is

(i) red or black

(ii) not black

105.

A coin is tossed 3 times. Find the probability of getting

(i) all heads (ii) atleast 2 heads

106.

Two dice are rolled once. Find the probability of getting such numbers on two dice, whose product is a perfect square.

107.

Two different dice are tossed together. Find the probability

(i) that the number on each die is even.

(ii) that the sum of numbers appearing on the two dice is 5.

108.

A letter is chosen at random from the letters of the word 'ASSASSINATION'. Find the probability that the letter chosen is a vowel.

109.

Five cards, ten, jack, queen, king and an ace of diamond are shuffled with their face downwards. One card is picked at random. What is the probability that

(i) the card is ten or jack? (ii) that the card is king?

110.

Two dice are thrown simultaneously. What is the probability that

(i) 3 will not come up on atleast one die?

(ii) 3 will come up on both dice?

111.

A box contains 80 dics numbered from 1 to 80. If one disc is drawn at random from the box, find the porbability that it bears

(i) a perfect square number

(ii) a number divisible by 2 and 3

112.

A card is drawn from a well-shuffled pack of 52 cards. Find the probability of getting

(i) a red face card (ii) a black king

(iii) either a spade or an ace

113.

A game consists of tossing a coin 3 times and noting its outcome each time. Hanif wins, if he ets three heads or three tails and losses otherwise. Calculate the probability that Hanif will win the game.

114.

A number is selected at random from the numbers 3, 5, 5, 7, 7, 7, 9, 9, 9, 9. Find the probability that the selected number is their average.

115.

Two dice are thrown at the same time. Determine the probability that the difference of the numbers on the two dice is 2.

116.

A box contains 12 balls out of which x are black. If one ball is drawn from the box, what is the probability that it will be a black ball. If 12 more black balls are put in the box, the probability of drawing a black ball now is double of what it was before. Find the value of x.

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