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General Probability PYQs

Class 10 Probability Board Questions (2014 – 2026)

Topic Overview

Master the basics. $P(E) + P(\bar{E}) = 1$. For Leap Years (366 days), the probability of 53 Sundays is $2/7$. For Non-Leap Years (365 days), it is $1/7$. Remember, probability $P$ always satisfies $0 \le P \le 1$.

Q1 2024
00:00
If $P(E) = 0.05$, what is the probability of 'not $E 00:00
If $P(E) = 0.05$, what is the probability of 'not $E
?
(a)(A) 0.05
(b)(B) 0.95
(c)(C) 0.09
(d)(D) 1.05
$P(\text{not } E) = 1 - P(E) = 1 - 0.05 = 0.95$.
Ans: (B) 0.95
Q2 2026
00:00
The probability that a non-leap year has 53 Sundays is:
(a)(A) 1/7
(b)(B) 2/7
(c)(C) 53/365
(d)(D) 0
Non-leap year has 365 days $= 52 \text{ weeks} + 1 \text{ day}$.
The extra day can be any of the 7 days of the week.
Probability of it being Sunday is 1/7.
Ans: (A) 1/7
Q3 2025
00:00
A card is drawn from a deck of 52 cards. Find the probability that the card drawn is: (i) a queen of black color (ii) either a king or a queen (iii) a spade
Total cards $= 52$.
(i) Black Queen: Spades and Clubs. Total 2. $P = 2/52 = 1/26$.
(ii) King or Queen: 4 Kings + 4 Queens. Total 8. $P = 8/52 = 2/13$.
(iii) Spade: Total 13. $P = 13/52 = 1/4$.
Ans: (i) 1/26, (ii) 2/13, (iii) 1/4
Q4 2022
00:00
Savita and Hamida are friends. What is the probability that both will have: (i) the same birthday? (ii) different birthdays? (ignoring leap year)
Total days $= 365$.
(i) Same Birthday: Only 1 outcome where both share the day. $P = 1/365$.
(ii) Different Birthdays: $P = 1 - 1/365 = 364/365$.
Ans: (i) 1/365, (ii) 364/365
Q5 2026
00:00
PASSAGE: Gaming Competition. In a school game, players draw two cards from a box containing cards numbered 1 to 20. The player wins if the product of the numbers on the two cards is a perfect square.
(i) If one card is drawn, what is the probability it is a prime number?
(ii) What is the probability that the number on the card is a multiple of 4?
(iii) If two cards are drawn (with replacement), find the probability that both have the same number (a doublet).
(i) Primes (2,3,5,7,11,13,17,19) $= 8$. $P = 8/20 = 2/5$.
(ii) Multiples of 4 (4,8,12,16,20) $= 5$. $P = 5/20 = 1/4$.
(iii) Total $= 20 \times 20 = 400$. Doublets $= 20$. $P = 20/400 = 1/20$.
?
(a)(A) 0.05
(b)(B) 0.95
(c)(C) 0.09
(d)(D) 1.05
$P(\text{not } E) = 1 - P(E) = 1 - 0.05 = 0.95$.
Ans: (B) 0.95
Q2 2026
00:00
The probability that a non-leap year has 53 Sundays is:
(a)(A) 1/7
(b)(B) 2/7
(c)(C) 53/365
(d)(D) 0
Non-leap year has 365 days $= 52 \text{ weeks} + 1 \text{ day}$.
The extra day can be any of the 7 days of the week.
Probability of it being Sunday is 1/7.
Ans: (A) 1/7
Q3 2025
00:00
A card is drawn from a deck of 52 cards. Find the probability that the card drawn is: (i) a queen of black color (ii) either a king or a queen (iii) a spade
Total cards $= 52$.
(i) Black Queen: Spades and Clubs. Total 2. $P = 2/52 = 1/26$.
(ii) King or Queen: 4 Kings + 4 Queens. Total 8. $P = 8/52 = 2/13$.
(iii) Spade: Total 13. $P = 13/52 = 1/4$.
Ans: (i) 1/26, (ii) 2/13, (iii) 1/4
Q4 2022
00:00
Savita and Hamida are friends. What is the probability that both will have: (i) the same birthday? (ii) different birthdays? (ignoring leap year)
Total days $= 365$.
(i) Same Birthday: Only 1 outcome where both share the day. $P = 1/365$.
(ii) Different Birthdays: $P = 1 - 1/365 = 364/365$.
Ans: (i) 1/365, (ii) 364/365
Q5 2026
00:00
PASSAGE: Gaming Competition. In a school game, players draw two cards from a box containing cards numbered 1 to 20. The player wins if the product of the numbers on the two cards is a perfect square.
(i) If one card is drawn, what is the probability it is a prime number?
(ii) What is the probability that the number on the card is a multiple of 4?
(iii) If two cards are drawn (with replacement), find the probability that both have the same number (a doublet).
(i) Primes (2,3,5,7,11,13,17,19) $= 8$. $P = 8/20 = 2/5$.
(ii) Multiples of 4 (4,8,12,16,20) $= 5$. $P = 5/20 = 1/4$.
(iii) Total $= 20 \times 20 = 400$. Doublets $= 20$. $P = 20/400 = 1/20$.
00:00
If $P(E) = 0.05$, what is the probability of 'not $E ?
(a)(A) 0.05
(b)(B) 0.95
(c)(C) 0.09
(d)(D) 1.05
$P(\text{not } E) = 1 - P(E) = 1 - 0.05 = 0.95$.
Ans: (B) 0.95
Q2 2026
00:00
The probability that a non-leap year has 53 Sundays is:
(a)(A) 1/7
(b)(B) 2/7
(c)(C) 53/365
(d)(D) 0
Non-leap year has 365 days $= 52 \text{ weeks} + 1 \text{ day}$.
The extra day can be any of the 7 days of the week.
Probability of it being Sunday is 1/7.
Ans: (A) 1/7
Q3 2025
00:00
A card is drawn from a deck of 52 cards. Find the probability that the card drawn is: (i) a queen of black color (ii) either a king or a queen (iii) a spade
Total cards $= 52$.
(i) Black Queen: Spades and Clubs. Total 2. $P = 2/52 = 1/26$.
(ii) King or Queen: 4 Kings + 4 Queens. Total 8. $P = 8/52 = 2/13$.
(iii) Spade: Total 13. $P = 13/52 = 1/4$.
Ans: (i) 1/26, (ii) 2/13, (iii) 1/4
Q4 2022
00:00
Savita and Hamida are friends. What is the probability that both will have: (i) the same birthday? (ii) different birthdays? (ignoring leap year)
Total days $= 365$.
(i) Same Birthday: Only 1 outcome where both share the day. $P = 1/365$.
(ii) Different Birthdays: $P = 1 - 1/365 = 364/365$.
Ans: (i) 1/365, (ii) 364/365
Q5 2026
00:00
PASSAGE: Gaming Competition. In a school game, players draw two cards from a box containing cards numbered 1 to 20. The player wins if the product of the numbers on the two cards is a perfect square.
(i) If one card is drawn, what is the probability it is a prime number?
(ii) What is the probability that the number on the card is a multiple of 4?
(iii) If two cards are drawn (with replacement), find the probability that both have the same number (a doublet).
(i) Primes (2,3,5,7,11,13,17,19) $= 8$. $P = 8/20 = 2/5$.
(ii) Multiples of 4 (4,8,12,16,20) $= 5$. $P = 5/20 = 1/4$.
(iii) Total $= 20 \times 20 = 400$. Doublets $= 20$. $P = 20/400 = 1/20$.