CBSE Class 9 Mathematics Probability MCQs Set 11

Download CBSE MCQs for Class 9 Mathematics: Chapter 15 Probability

Explore reliable objective questions for Chapter 15 Probability tailored for Class 9 learners. Utilizing these Mathematics multiple-choice formats ensures thorough preparation and strengthens problem-solving speed for upcoming school assessments.

Chapter-wise Objective Questions: Chapter 15 Probability

Access the complete set of multiple-choice questions for Chapter 15 Probability below. This focused format allows students to isolate specific topics for thorough review and uninterrupted practice alongside official CBSE textbooks.

Multiple Choice Questions

Question 1: The number of triangles that can be formed by joining the vertices of a heptagon is
(a) 49
(b) 35
(c) 71
(d) 25
Show Answer & Explanation

Answer: (b) 35

Explanation:
1. Choose any 3 of the 7 vertices: C(7,3) = 7·6·5 ÷ 6 = 35.
2. No three vertices of a convex polygon are collinear.

Teacher's Note:
1. Combination, not permutation.

Question 2: The number of diagonals in an n-sided polygon (n > 3) is
(a) C(n,2) − n
(b) C(n,2)
(c) n · C(n−1, 2)
(d) C(n, n−2)
Show Answer & Explanation

Answer: (a) C(n,2) − n

Explanation:
1. Any two vertices give a segment: C(n,2).
2. Of these, n are sides, so diagonals = C(n,2) − n = n(n − 3)/2.

Teacher's Note:
1. Check with n = 4: 6 − 4 = 2.

Question 3: A family has seven children: five boys and two girls (the female to male ratio in the family of nine, including both parents, is 1 : 2). The probability that all the children are of the same sex is
(a) 0
(b) 2/5
(c) 1/21
(d) 5!/7!
Show Answer & Explanation

Answer: (a) 0

Explanation:
1. The family has both boys and girls, so all seven cannot be of the same sex.
2. The event is impossible, so the probability is 0.

Teacher's Note:
1. An impossible event has probability 0.

Question 4: A family has seven children: five boys and two girls (the female to male ratio in the family of nine, including both parents, is 1 : 2). If the order of birth is random, the probability that the five oldest are boys and the youngest two are girls is
(a) 0
(b) 2/5
(c) 1/21
(d) 5!/7!
Show Answer & Explanation

Answer: (c) 1/21

Explanation:
1. The two girls can occupy any 2 of 7 birth positions: C(7,2) = 21 equally likely arrangements.
2. Only one arrangement has the girls youngest: 1/21.

Teacher's Note:
1. Count positions of the girls.

Question 5: When two dice are thrown simultaneously, the probability that exactly one 5 appears is
(a) 4/36
(b) 5/18
(c) 6/23
(d) 7/24
Show Answer & Explanation

Answer: (b) 5/18

Explanation:
1. Exactly one 5: (5, x) or (x, 5) with x ≠ 5: 5 + 5 = 10 outcomes.
2. P = 10/36 = 5/18.

Teacher's Note:
1. Do not count (5, 5).

Question 6: When two fair dice are thrown, the probability that both show even numbers is
(a) 1/2
(b) 1/4
(c) 1/3
(d) 1/5
Show Answer & Explanation

Answer: (b) 1/4

Explanation:
1. Even numbers: 2, 4, 6, so 3 × 3 = 9 outcomes.
2. P = 9/36 = 1/4.

Teacher's Note:
1. Each die is independent.

Question 7: A card is drawn from a pack of 52. The probability that it is black is
(a) 1/2
(b) 1/13
(c) 1/26
(d) 7/13
Show Answer & Explanation

Answer: (a) 1/2

Explanation:
1. 26 of the 52 cards are black: 26/52 = 1/2.

Teacher's Note:
1. Spades and clubs are black.

Question 8: A card is drawn from a pack of 52. The probability that it is a queen is
(a) 1/2
(b) 1/13
(c) 1/26
(d) 7/13
Show Answer & Explanation

Answer: (b) 1/13

Explanation:
1. There are 4 queens: 4/52 = 1/13.

Teacher's Note:
1. One queen per suit.

Question 9: A card is drawn from a pack of 52. The probability that it is a black queen is
(a) 1/2
(b) 1/13
(c) 1/26
(d) 7/13
Show Answer & Explanation

Answer: (c) 1/26

Explanation:
1. The black queens are the queen of spades and the queen of clubs: 2/52 = 1/26.

Teacher's Note:
1. Two black suits.

Question 10: A card is drawn from a pack of 52. The probability that it is black or a queen is
(a) 1/2
(b) 1/13
(c) 1/26
(d) 7/13
Show Answer & Explanation

Answer: (d) 7/13

Explanation:
1. Black cards = 26, queens = 4, black queens = 2.
2. Favourable = 26 + 4 − 2 = 28, so P = 28/52 = 7/13.

Teacher's Note:
1. Avoid counting the black queens twice.

Question 11: Three fair dice are thrown. The probability that the sum is at least 6 is
(a) 103/216
(b) 103/108
(c) 47/216
(d) None of these
Show Answer & Explanation

Answer: (b) 103/108

Explanation:
1. Total outcomes = 216. Sum less than 6 means sums 3, 4, 5: 1 + 3 + 6 = 10 outcomes.
2. P(at least 6) = 1 − 10/216 = 206/216 = 103/108.

Teacher's Note:
1. Sums 3, 4, 5 give 1, 3 and 6 outcomes, so 10 in all.

Question 12: Two coins are such that the first has a head and a tail and the second has heads on both sides. One of the coins is chosen at random and tossed, and the result is a head. The probability that it was the two-headed coin is
(a) 1/2
(b) 1/3
(c) 2/3
(d) 2/7
Show Answer & Explanation

Answer: (c) 2/3

Explanation:
1. Possible equally likely head outcomes: coin 1 head (1/4 of cases), coin 2 head (1/2 of cases).
2. P(coin 2 | head) = (1/2) ÷ (1/4 + 1/2) = 2/3.
3. Equivalently, of the three equally likely heads, two are on the double-headed coin.

Teacher's Note:
1. Count the faces showing heads: three in all.

Question 13: Three coins are tossed. The probability of getting neither 3 heads nor 3 tails is
(a) 1/2
(b) 1/3
(c) 2/3
(d) 3/4
Show Answer & Explanation

Answer: (d) 3/4

Explanation:
1. Total 8 outcomes; HHH and TTT are 2 of them.
2. P = 6/8 = 3/4.

Teacher's Note:
1. Use the complement.

Question 14: A and B are events with P(A) = 0.5, P(B) = 0.3 and P(A and B) = 0.2. Then P(A or B) is
(a) 0.4
(b) 0.3
(c) 0.6
(d) 0.9
Show Answer & Explanation

Answer: (c) 0.6

Explanation:
1. P(A or B) = P(A) + P(B) − P(A and B) = 0.5 + 0.3 − 0.2 = 0.6.

Teacher's Note:
1. Subtract the overlap once.

Question 15: A and B are mutually exclusive events with P(A) = 1/2 and P(B) = 1/3. Then P(A or B) is
(a) 5/6
(b) 3/4
(c) 2/3
(d) None of these
Show Answer & Explanation

Answer: (a) 5/6

Explanation:
1. For mutually exclusive events P(A or B) = P(A) + P(B) = 1/2 + 1/3 = 5/6.

Teacher's Note:
1. No overlap to subtract.

Question 16: Two dice are thrown. The probability that the sum is neither 3 nor 4 is
(a) 31/36
(b) 4/9
(c) 5/36
(d) 1/3
Show Answer & Explanation

Answer: (a) 31/36

Explanation:
1. Sum 3: (1,2), (2,1). Sum 4: (1,3), (3,1), (2,2). That is 5 outcomes.
2. P = 1 − 5/36 = 31/36.

Teacher's Note:
1. Use the complement.

Question 17: Three identical dice are rolled. The probability that the same number appears on each is
(a) 1/6
(b) 6/216
(c) 1/216
(d) 3/28
Show Answer & Explanation

Answer: (b) 6/216

Explanation:
1. The favourable outcomes are (1,1,1) ... (6,6,6): 6 of 216.
2. P = 6/216 = 1/36.

Teacher's Note:
1. Do not confuse with the chance of one given triple.

Question 18: Which of the following cannot be the probability of an event?
(a) 2/3
(b) 7/5
(c) 1/2
(d) 15%
Show Answer & Explanation

Answer: (b) 7/5

Explanation:
1. A probability lies between 0 and 1. 7/5 = 1.4 exceeds 1.
2. 2/3, 1/2 and 15% = 0.15 are all valid.

Teacher's Note:
1. Probability is at most 1.

Question 19: A card is drawn from a pack of 52 and a gambler bets that it is a spade or an ace. The odds against his winning are
(a) 4 : 9
(b) 7 : 6
(c) 9 : 4
(d) 8 : 5
Show Answer & Explanation

Answer: (c) 9 : 4

Explanation:
1. Favourable = 13 + 4 − 1 = 16, so P(win) = 16/52 = 4/13.
2. Odds against = 9 : 4.

Teacher's Note:
1. Odds against = failures : successes.

Question 20: The probability of getting a number greater than 2 in a throw of a die is
(a) 1/3
(b) 2/3
(c) 1/2
(d) 5/6
Show Answer & Explanation

Answer: (b) 2/3

Explanation:
1. Favourable: 3, 4, 5, 6 so 4/6 = 2/3.

Teacher's Note:
1. Do not include 2.

Question 21: Two dice are rolled together. The probability of a total of 9 is
(a) 1/3
(b) 1/9
(c) 8/9
(d) 9/10
Show Answer & Explanation

Answer: (b) 1/9

Explanation:
1. Sum 9: (3,6), (4,5), (5,4), (6,3): 4/36 = 1/9.

Teacher's Note:
1. Count ordered pairs.

Question 22: Two dice are rolled together. The probability of a sum greater than 9 is
(a) 10/11
(b) 5/6
(c) 1/6
(d) 8/9
Show Answer & Explanation

Answer: (c) 1/6

Explanation:
1. Sum 10: 3, sum 11: 2, sum 12: 1, so 6 outcomes.
2. P = 6/36 = 1/6.

Teacher's Note:
1. List the sums 10, 11, 12.

Question 23: Two dice are rolled together. The probability of a total of 9 or 11 is
(a) 2/99
(b) 20/99
(c) 1/6
(d) 1/10
Show Answer & Explanation

Answer: (c) 1/6

Explanation:
1. Sum 9: 4 outcomes; sum 11: 2 outcomes.
2. P = 6/36 = 1/6.

Teacher's Note:
1. The events are mutually exclusive.

Question 24: Two dice are rolled together. The probability of a doublet is
(a) 1/12
(b) 0
(c) 5/8
(d) 1/6
Show Answer & Explanation

Answer: (d) 1/6

Explanation:
1. Doublets (1,1) ... (6,6): 6 of 36 = 1/6.

Teacher's Note:
1. Same number on both dice.

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Chapter 15 Probability Objective Questions & Solutions for Class 9 Mathematics

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FAQs

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