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King, queen and jack of hearts are removed from a pack of 52 playing cards and then the pack is well shuffled. A card is drawn from the remaining cards. Find the probability of getting a card of
(a) hearts
(b) a queen
(c) not a king
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Total outcome = 49
(i) P(getting a heart)
(ii) P(getting a queen card)
P(not a king card)
All the three face cards of spades are removed from a wellshuffled pack of 52 cards. A card is then drawn at random from the remaining pack. Find the probability of getting
(a) a black face card
(b) a queen
(c) a black card
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Total cards left
(i) P(black face card)
(ii) P(queen)
(iii) P(a black card)
A bag contains cards numbered from 1 to 25, one card is drawn at random from the bag. Find the probability that this card has a number which is divisible by both 2 and 3.
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Total cards = 25
Multiple of 2 and 3 = 6, 12, 18, 24
Cards numbered from 1 to 64 are placed in a box. A card is drawn at random from the box. Find the probability that the card number on the card drawn is a perfect cube.
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Total cards = 64
Number of favourable outcomes = 1, 18, 27, 64
A box contains 20 balls, bearing numbers 1, 2, 3, 4, ……20. A ball is drawn at random from the box. What is the probability that the number on the drawn ball is :
(a) add odd number
(b) divisible for 2 or 3
(c) prime number
(d) not divisible by 10
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Total outcomes = 20
(i) P(getting an odd number)
(ii) P(getting a number divisible by 2 or 3)
(iii) P(getting a prime number)
(iv) P(getting a number divisible by 10)
P(not divisible by 10)
Two dice are thrown at the same time. Write down all the possible outcomes. What is the probability that the two numbers appearing on the top of the dice
(a) are prime ?
(b) has the sum less than or equal to 12 ?
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All possible outcomes = (1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,1), (2,2), (2,3), (2,4), (2,5), (2,6), (3,1), (3,2), (3,3), (3,4), (3,5), (3,6), (4,1), (4,2), (4,3), (4,4), (4,5), (4,6), (5,1), (5,2), (5,3), (5,4), (5,5), (5,6), (6,1), (6,2), (6,3), (6,4), (6,5), (6,6)
(i) P(are prime)
(ii) P(sum less than or equal to 12)
Two dice are thrown together. Find the probability that the product of the numbers on the top of the dice is :
(a) 6
(b) 12
(c) 7
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Total outcomes = 36
(i) P(Product 36)
(ii) P(Product is 12)
(iii) P(Product is 7)
A bag contains 5 white balls, 7 red balls, 4 black balls and 2 blue balls. One ball is drawn at random from the bag. What is the probability that the ball drawn is :
(a) white or blue
(b) not white
(c) neither white nor black
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Total balls
(i) P(white or blue)
(ii) P(not white)
(iii) P(neither white nor black)
Two dice are thrown simultaneously. Find the probability of getting :
(a) same number on both dice.
(b) different numbers on both the dice.
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(i) P(same number on both dice)
(ii) P(different number on both dice)
Cards marked with numbers 13, 14, 15, …., 60 are placed in a box and mixed thoroughly. One card is drawn at random from the box. Find the probability that the number on the drawn card is
(a) divisible by 5
(b) a number which is a perfect square.
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Total outcomes = 48
(i) P(divisible by 5)
(ii) P(getting a perfect square number)
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. What is the probability that both will visit the shop on
(a) the same day ?
(b) consecutive days
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Total outcomes
(i) P(on the same day)
(ii) P(on consecutive day)
All the face cards of spades are removed from a pack of 52 playing cards and then the pack is shuffled well. A card is then drawn at random from the remaining pack of cards. Find the probability of getting
(a) a black face card,
(b) a queen.
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Total cards left = 49
P(black face card)
P(queen)
An urn contains 8 red, 6 white and 4 black balls. A ball is drawn at random from the urn. Find the probability that the drawn ball is :
(a) red or white
(b) neither black nor white
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Total balls
(i) P(red or white)
(ii) P(neither black nor white)
A child has a die whose six faces show the letters as given below : A B C D E A
The die is thrown at random once. What is the probability of getting
(a) A
(b) E.
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P(getting A)
(ii) P(getting E)
From a well shuffled pack of 52 cards, two black kings and two black jacks are removed. From the remaining cards, a card is drawn at random. Find the probability that the drawn card is not a king.
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Number of cards left = 48
P(drawing a king)
Required probability
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 :
(a) a twodigit number.
(b) a perfect square number.
(c) a number divisible by 5.
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Total outcomes = 90
(i) P(getting a two digit numbers)
(ii) P(getting a perfect square)
(iii) P(getting a number divisible by 5)
A pair of dice is thrown once.
(a) Write sample space for the experiment.
(b) Find the probability of getting an odd number on each dice.
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(a) Sample space = 36
(b) P(getting odd number)
From a bag containing 5 red, 6 black and 7 yellow balls, a ball is drawn at random. Find the probability that it is :
(a) not yellow ball
(b) neither black nor red
(c) either black or yellow
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Total balls
(i) P(not yellow)
(ii) P(neither black nor red)
(iii) P(either black or yellow)
A bag contains 18 balls, out of which x balls are red.
(a) If one ball is drawn at random from the bag, what is probability that it is a red ball.
(b) If 2 more red balls are put in the bag, the probability of drawing a red ball will be \(\dfrac{9}{8} \) times that of the probability of red ball coming in part (a). Find x.
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(a) P(red ball)
(b) Total balls
A/Q
Three unbiased coins are tossed. What is the probability of getting
(a) two heads
(b) at least two heads
(c) at most two heads
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(a) P(getting 2 heads)
(b) P(at least 2 heads)
(c) P(at most 2 heads)
From a well shuffled pack of 52 playing cards, black jacks, black kings and black aces are removed. A card is then drawn at random from the remaining pack. Find the probability of getting.
(a) a red card
(b) not a diamond card
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Remaining cards after removal
(i) P(red card)
(ii) P(not a diamond card)
A box contains 12 balls out of which x are black. If one ball is drawn at random from the box, what is the prbability that it will be a black ball ? If 6 more black balls are put in the box, the probability of drawing a black ball now is double of what it was before. Find x.
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P(drawing a black ball)
Also
P(drawing a black ball)
A/Q
A bag contains 5 white balls, 7 red balls, 4 black balls and 2 blue balls. One ball is drawn at random from the bag. What is the probability that the ball drawn is :
(a) white or blue
(b) red or black
(c) not white
(d) neither white not black.
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Total balls
(i) P(white or blue)
(ii) P(red or black)
(iii) P(not white)
(iv) P(neither white nor black)
A card is drawn at random from a wellshuffled deck of playing cards. Find the probability that the card drawn is :
(a) a king or a jack
(b) a nonace
(c) a red card
(d) neither a king nor a queen.
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(a) P(King or jack)
(b) P(a ace)
(iii) P(a nonace)
(c) P(red card)
(d) P(neither king nor queen)
Find the probability that a number selected at random from the number 1, 2, 3, ….., 35 is a
(a) prime number
(b) multiple of 7
(c) multiple of 3 or 5.
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(a) Total outcomes = 35
Total favourable outcomes = 11
(b) Total favourable outcomes = 5
(c) Total favourable outcomes = 16
From a pack of 52 playing cards, jacks, queens, kings and aces of red colour are removed. From the remaining a card is drawn at random. Find the probability that the card drawn is :
(a) a black queen
(b) a red card
(c) a black jack
(d) a picture card (jacks, queens and kings are picture cards)
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Remaining card
(a) No. of black queen = 2
(b) No. of red cards left
(c) P(Jack)
(d) No. of picture cards left
A bag conains 5 red balls and some blue balls. If the probability of drawing a blue ball from the bag is thrice that of a red ball, find the number of blue balls in the bag.
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Total no. of balls
Probability of drawing a red ball
Probability of drawings a blue ball
A/Q
No. of blue balls = 15
A box contains 5 red balls 4 green balls and 7 white balls. A ball is drawn at random from the box. Find the probability that the ball drawn is :
(a) white
(b) neither red nor white
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Total balls
(a) P(white)
(b) P(neither red nor white)
All the three face cards of spades are removed from a wellshuffled pack of 52 cards. A card is then drawn at random from the remaining pack. Find the probability of getting
(a) a black face card
(b) a queen
(c) a black card.
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Total cards left = 49
(a) P(black face card)
(b) P(queen)
(c) P(black card)
A box has cards numbered 14 to 99. Cards are mixed thoroughly and a card is drawn from the bag at random. Find the probability that the number on the card, drawn from the box is :
(a) an odd number
(b) a perfact square number
(c) a number divisible by 7.
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Total cards
(a) odd no.
P(odd no.)
(b) P(Perfect square)
(c) P(divisible by 7)