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Coins and Dice PYQs

Class 10 Probability Board Questions (2014 – 2026)

Topic Overview

Master the Sample Spaces. For 2 Coins ($n=4$), 3 Coins ($n=8$). For 2 Dice ($n=36$). Remember: Product is Prime means the result must be 2, 3, or 5.

Q1 2026
00:00
Two different dice are thrown together. The probability that the product of the numbers appearing on them is a prime number is:
(a)(A) 1/6
(b)(B) 1/12
(c)(C) 1/9
(d)(D) 5/36
Total outcomes $= 36$. Primes: (1,2), (1,3), (1,5), (2,1), (3,1), (5,1).
Prob $= 6/36 = 1/6$.
Ans: (A) 1/6
Q2 2025
00:00
Three coins are tossed simultaneously. The probability of getting at least two heads is:
(a)(A) 1/2
(b)(B) 3/8
(c)(C) 5/8
(d)(D) 1/4
At least 2 heads: HHH, HHT, HTH, THH. Prob $= 4/8 = 1/2$.
Ans: (A) 1/2
Q3 2024
00:00
The probability of getting a sum of 13 in a single throw of two dice is:
(a)(A) 1/36
(b)(B) 1
(c)(C) 0
(d)(D) 1/12
Max sum is 12 ($6+6$). Sum 13 is impossible.
Ans: (C) 0
Q4 2024
00:00
Two dice are thrown at the same time. Find the probability of getting: (i) a total of 10 (ii) a doublet (iii) a sum less than 5
(i) Sum 10: 3/36. (ii) Doublet: 6/36. (iii) Sum < 5: 6/36.
Ans: (i) 1/12, (ii) 1/6, (iii) 1/6
Q5 2021
00:00
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.
(i) Both Even: (2,2), (2,4), (2,6), (4,2), (4,4), (4,6), (6,2), (6,4), (6,6). Total 9. $P = 9/36 = 1/4$.
(ii) Sum 5: (1,4), (2,3), (3,2), (4,1). Total 4. $P = 4/36 = 1/9$.
Ans: (i) 1/4, (ii) 1/9
Q6 2026
00:00
Two dice are thrown simultaneously. What is the probability that: (i) 5 will not come up on either of them? (ii) 5 will come up at least once?
Total outcomes $= 36$.
(ii) 5 at least once: (5,1..6) and (1..6,5). Total $6+6-1 = 11$. $P = 11/36$.
(i) 5 not at all: $1 - 11/36 = 25/36$.
Ans: (i) 25/36, (ii) 11/36
00:00
Two different dice are thrown together. The probability that the product of the numbers appearing on them is a prime number is:
(a)(A) 1/6
(b)(B) 1/12
(c)(C) 1/9
(d)(D) 5/36
Total outcomes $= 36$. Primes: (1,2), (1,3), (1,5), (2,1), (3,1), (5,1).
Prob $= 6/36 = 1/6$.
Ans: (A) 1/6
Q2 2025
00:00
Three coins are tossed simultaneously. The probability of getting at least two heads is:
(a)(A) 1/2
(b)(B) 3/8
(c)(C) 5/8
(d)(D) 1/4
At least 2 heads: HHH, HHT, HTH, THH. Prob $= 4/8 = 1/2$.
Ans: (A) 1/2
Q3 2024
00:00
The probability of getting a sum of 13 in a single throw of two dice is:
(a)(A) 1/36
(b)(B) 1
(c)(C) 0
(d)(D) 1/12
Max sum is 12 ($6+6$). Sum 13 is impossible.
Ans: (C) 0
Q4 2024
00:00
Two dice are thrown at the same time. Find the probability of getting: (i) a total of 10 (ii) a doublet (iii) a sum less than 5
(i) Sum 10: 3/36. (ii) Doublet: 6/36. (iii) Sum < 5: 6/36.
Ans: (i) 1/12, (ii) 1/6, (iii) 1/6
Q5 2021
00:00
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.
(i) Both Even: (2,2), (2,4), (2,6), (4,2), (4,4), (4,6), (6,2), (6,4), (6,6). Total 9. $P = 9/36 = 1/4$.
(ii) Sum 5: (1,4), (2,3), (3,2), (4,1). Total 4. $P = 4/36 = 1/9$.
Ans: (i) 1/4, (ii) 1/9
Q6 2026
00:00
Two dice are thrown simultaneously. What is the probability that: (i) 5 will not come up on either of them? (ii) 5 will come up at least once?
Total outcomes $= 36$.
(ii) 5 at least once: (5,1..6) and (1..6,5). Total $6+6-1 = 11$. $P = 11/36$.
(i) 5 not at all: $1 - 11/36 = 25/36$.
Ans: (i) 25/36, (ii) 11/36