CBSE Class 10 Mathematics Probability VBQs Set B

Question. Two dice are thrown at the same time, what is the probability that the sum appearing on the two top 8 is -------
(a) 5/8
(b) 5/36
(c) 5/12
(d) None
Answer : B

Question. One card is drawn from a well-shuffled deck of 52 cards. Find the probability of getting a king of red colour
(a) 1/26
(b) 2/13
(c) 1/13
(d) 3/26
Answer : A

Question. The probability of getting a bad egg in a lot of 400 is 0.035. The number of bad eggs in the lot is
(a) 7
(b) 14
(c) 21
(d) 28
Answer : B

Question. Which of the following never be the probability of an event of any random experiment.
(a) 112%
(b) 7/5
(c) -0.3%
(d) all of these
Answer : D

Question. A bag contains 40 balls out of which some are red, some are blue and remaining are black. If the probability of drawing a red ball is 11/20 and that of blue ball is 1/5 , then what is the no. of black ball.
(a) 5
(b) 10
(c) 15
(d) 20
Answer : B

Question. A coin is flipped to decide which team starts the game. What is the probability of your team will start?
(a) 1/4
(b) 1/2
(c) 1
(d) 0
Answer : B

Question. In a lottery, there are 10 prizes and 25 blanks. Find the probability of getting a prize.
(a) 2/7
(b) 5/7
(c) 3/7
(d) None
Answer : A

Question. Out of first 24 tickets 14 males have already won the ticket and remaining are won by females. Chances that last ticket is won by Geeta is.
( a) 24/25
(b) 11990/20000
(c) 1/19976
(d) 11990/19976
Answer : C

Question. How many more males should have sent SMS`s so that the chances of winning a ticket is equal for both male/female
( a) 4000
(b) 2000
(c) 12000
(d) cannot be determined
Answer : A

Question. In the same condition, the number of winner tickets is doubled and one ticket is left for male while rest are won by female. Find the probability of winning last ticket by any male.
(a) 1/19951
(b) 1/8000
(c) 8000/19951
(d) cannot be determined
Answer : C

Case Study 1:

Most People use playing card decks just for fun and to spend time. However, there are many benefits of playing cards. It improves patience, concentration and boosts memory skills. All these help everyone in their daily life. It helps to make people socialized and help to connect with people of all mindset.

Three friends play a game with playing cards. They remove Red and black colour of king , queen and ace from a pack of 52 playing cards.
Based on the above information, answer the following questions.

(i) Find the probability of red colour card from the pack.
Answer : 1/2)

(ii) Find the probability of getting a spade.
Answer : 1/4)

(iii) Find the probability of getting jack of red colour.
Answer : 1/20)

Case Study 2:
Playing cards
Four persons are playing a bridge game forming teams each of two players. A deck of 52 playing cards is distributed around the table clockwise in such a way that each person gets 13 cards.

(i) Find the probability of the card drawn by each player with number 5 or 6.
(a) 2/13
(b) 11/13
(c) 1/13
(d) 12/13
Answer : A

(ii) Find the probability of the card drawn by each player with number less than 8.
(a) 6/13
(b) 5/13
(c) 7/13
(d) None of these
Answer : C

(iii) Find the probability of the card drawn by each player with number between 2 and 9.
(a) 7/13
(b) 5/13
(c) 6/13
(d) 3/13
Answer : C

(iv) What is the probability that any one person gets queen of spade?
(a) 1/3
(b) 1/4
(c) 1/2
(d) 1
Answer : B

Assertion and Reason Questions

Question. Assertion: If a box contains 5 white, 2 red and 4 black marbles, then the probability of not drawing a White marble from the box is 5/11 .
Reason: P (Not E) () = 1 - P (E) , where E is any event.
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true
Answer : D

Question. Assertion: The probability of winning a game is 0.4, then the probability of losing it, is 0.6
Reason: P (E) + P (not E) = 1
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true
Answer : A

Very Short Answer type Questions

Question. A bag contains 15 white and some black balls. If the probability of drawing a black ball from the bag is thrice that of drawing a white ball, find the number of black balls in the bag.
Answer : 45

Question. A coin is tossed two times. Find the probability of getting both heads or both tails
Answer : 1/2

Question. A group consists of 12 persons, out of which 4 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.
Answer : 1/3 (ii) 2/3

Question. A card is drawn from a well – shuffled pack of 52 cards. Find the probability that the card drawn is either a red card or a queen
Answer : 7/13

Question. A card is drawn from a well – shuffled pack of 52 cards. Find the probability of getting
(i) a red king
(ii) a queen or jack
Answer : 1/26 (ii) 2/13

Question. A pair of dice is thrown once. Find the probability of getting
(i) doublet of prime numbers
(ii) a doublet of odd numbers.
Answer : 1/12, 1/12

Question. In a family of 3 children calculate the probability of having at least one boy.
Answer : 7/8

Question. 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 cards
(ii) a queen
(iii) a black card
Answer : 3/49, 3/49, 23/49

Question. 12 defective pens are 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 the lot .Determine the probability that the pen taken out is a good one
Answer : 11/12

Question. From a bag containing 5 red , 8 black and 7 blue balls , a ball selected at random .Find the probability that
(i) it is not a red ball
(ii) it is a blue ball
Answer : 3/4 (ii) 27/20

Question. 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?
(III) Vowels:
Answer : 1/3 , 1/6 , 1/2

Question. A number x is selected at random from the numbers 1 , 4 , 9 , 16 and another number y is selected at random from numbers 1 , 2 ,3 4 . Find the probability that the value of xy is more than 16
Answer : 3/8

Question. 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
Answer : 7/9 , 5/9

Question. A box contains cards bearing numbers 6 to 70. If one card is drawn at random from the box ,find the probability that it bears
(a) not a one digit number
(b) a number not divisible by 5
(c) number is a perfect square
Answer : 61/65, 52/65, 6/65