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Cards and Selection PYQs

Class 10 Probability Board Questions (2014 – 2026)

Topic Overview

Know your deck: 52 cards, 2 colors, 4 suits, 12 Face Cards ($J, Q, K$). For bag problems, use the equation $P(\text{event}) = \text{Favorable} / \text{Total}$. Pay attention to "Replacement" vs "No Replacement" (though mostly simple cases are asked in Class 10).

Q1 2026
00:00
One card is drawn from a well-shuffled deck of 52 cards. The probability that it is a red face card is:
(a)(A) 3/26
(b)(B) 3/13
(c)(C) 1/13
(d)(D) 1/2
Total 52. Red face cards (J,Q,K of Hearts/Diamonds) $= 6$. $P = 6/52 = 3/26$.
Ans: (A) 3/26
Q2 2024
00:00
A card is drawn at random from a well-shuffled deck of 52 playing cards. The probability of getting a face card is:
(a)(A) 1/13
(b)(B) 3/13
(c)(C) 4/13
(d)(D) 1/4
Total face cards (J, Q, K in 4 suits) $= 12$. $P = 12/52 = 3/13$.
Ans: (B) 3/13
Q3 2022
00:00
All the black face cards are removed from a pack of 52 playing cards. The remaining cards are well shuffled and then a card is drawn at random. Find the probability of getting: (i) a face card (ii) a red card (iii) a black card
Removed: 6 black face cards (2J, 2Q, 2K). Remaining $= 46$.
(i) Face card: Only red ones left $= 6$. $P = 6/46 = 3/23$.
(ii) Red card: All 26 red cards are there. $P = 26/46 = 13/23$.
(iii) Black card: Remaining $= 26-6 = 20$. $P = 20/46 = 10/23$.
Ans: (i) 3/23, (ii) 13/23, (iii) 10/23
Q4 2025
00:00
A box contains cards numbered 11 to 60. A card is drawn at random from the box. Find the probability that the number on the drawn card is: (i) an odd number (ii) a perfect square number (iii) a number divisible by 5 (iv) a prime number less than 20
Total cards $= 60-11+1 = 50$.
(i) Odd: (11, 13, ..., 59) Total 25. $P = 25/50 = 1/2$.
(ii) Perfect Squares: (16, 25, 36, 49) Total 4. $P = 4/50 = 2/25$.
(iii) Divisible by 5: (15, 20, ..., 60) Total 10. $P = 10/50 = 1/5$.
(iv) Primes < 20: (11, 13, 17, 19) Total 4. $P = 4/50 = 2/25$.
Ans: (i) 1/2, (ii) 2/25, (iii) 1/5, (iv) 2/25
00:00
One card is drawn from a well-shuffled deck of 52 cards. The probability that it is a red face card is:
(a)(A) 3/26
(b)(B) 3/13
(c)(C) 1/13
(d)(D) 1/2
Total 52. Red face cards (J,Q,K of Hearts/Diamonds) $= 6$. $P = 6/52 = 3/26$.
Ans: (A) 3/26
Q2 2024
00:00
A card is drawn at random from a well-shuffled deck of 52 playing cards. The probability of getting a face card is:
(a)(A) 1/13
(b)(B) 3/13
(c)(C) 4/13
(d)(D) 1/4
Total face cards (J, Q, K in 4 suits) $= 12$. $P = 12/52 = 3/13$.
Ans: (B) 3/13
Q3 2022
00:00
All the black face cards are removed from a pack of 52 playing cards. The remaining cards are well shuffled and then a card is drawn at random. Find the probability of getting: (i) a face card (ii) a red card (iii) a black card
Removed: 6 black face cards (2J, 2Q, 2K). Remaining $= 46$.
(i) Face card: Only red ones left $= 6$. $P = 6/46 = 3/23$.
(ii) Red card: All 26 red cards are there. $P = 26/46 = 13/23$.
(iii) Black card: Remaining $= 26-6 = 20$. $P = 20/46 = 10/23$.
Ans: (i) 3/23, (ii) 13/23, (iii) 10/23
Q4 2025
00:00
A box contains cards numbered 11 to 60. A card is drawn at random from the box. Find the probability that the number on the drawn card is: (i) an odd number (ii) a perfect square number (iii) a number divisible by 5 (iv) a prime number less than 20
Total cards $= 60-11+1 = 50$.
(i) Odd: (11, 13, ..., 59) Total 25. $P = 25/50 = 1/2$.
(ii) Perfect Squares: (16, 25, 36, 49) Total 4. $P = 4/50 = 2/25$.
(iii) Divisible by 5: (15, 20, ..., 60) Total 10. $P = 10/50 = 1/5$.
(iv) Primes < 20: (11, 13, 17, 19) Total 4. $P = 4/50 = 2/25$.
Ans: (i) 1/2, (ii) 2/25, (iii) 1/5, (iv) 2/25