Board Previous Year Questions (Board PYQs)

Board Previous Year Questions

PYQ 1 (1 mark): The probability of a sure event is: (A) 0 (B) $\dfrac12$ (C) 1 (D) $-1$. [CBSE] Solution: 1. Answer: (C).

PYQ 2 (1 mark): Which cannot be the probability of an event? (A) 0.7 (B) $\dfrac{2}{3}$ (C) $-1.5$ (D) 0.15. [CBSE] Solution: $-1.5<0$. Answer: (C).

PYQ 3 (1 mark): A die is thrown once. The probability of getting a prime number is: (A) $\dfrac13$ (B) $\dfrac12$ (C) $\dfrac23$ (D) $\dfrac16$. [CBSE] Solution: primes $\{2,3,5\}$: $\dfrac12$. Answer: (B).

PYQ 4 (2 marks): Two coins are tossed simultaneously. Find the probability of getting at most one head. [CBSE] Solution: At most one head $=\{HT,TH,TT\}$: $\dfrac34$. Answer: $\dfrac34$.

PYQ 5 (2 marks): A card is drawn from a well-shuffled deck of 52 cards. Find the probability that it is a face card. [CBSE] Solution: $\dfrac{12}{52}=\dfrac{3}{13}$. Answer: $\dfrac{3}{13}$.

PYQ 6 (2 marks): One card is drawn from 52. Find the probability that it is neither a king nor a queen. [CBSE] Solution: $52-8=44$: $\dfrac{44}{52}=\dfrac{11}{13}$. Answer: $\dfrac{11}{13}$.

PYQ 7 (3 marks): Two dice are thrown together. Find the probability that the sum is (i) 7, (ii) a prime, (iii) at least 10. [CBSE] Solution: (i) $\dfrac6{36}=\dfrac16$; (ii) prime sums 2,3,5,7,11 → 15 ways → $\dfrac{15}{36}=\dfrac5{12}$; (iii) sums 10,11,12 → 6 ways → $\dfrac16$. Answers: $\dfrac16,\ \dfrac5{12},\ \dfrac16$.

PYQ 8 (3 marks): A bag contains 5 red, 8 white and 7 black balls. A ball is drawn at random. Find the probability that it is (i) red, (ii) not black. [CBSE] Solution: total 20. (i) $\dfrac{5}{20}=\dfrac14$; (ii) $1-\dfrac{7}{20}=\dfrac{13}{20}$. Answers: $\dfrac14,\ \dfrac{13}{20}$.

PYQ 9 (3 marks): A number is selected at random from 1 to 30. Find the probability that it is (i) a prime number, (ii) a multiple of 7. [CBSE] Solution: (i) primes up to 30: 2,3,5,7,11,13,17,19,23,29 → 10 → $\dfrac{10}{30}=\dfrac13$; (ii) $7,14,21,28$ → 4 → $\dfrac{4}{30}=\dfrac2{15}$. Answers: $\dfrac13,\ \dfrac2{15}$.

PYQ 10 (2 marks): If $P(E)=0.05$, what is the probability of 'not $E$'? [CBSE] Solution: $1-0.05=0.95$. Answer: 0.95.

PYQ 11 (3 marks): All kings and queens are removed from a deck. A card is drawn from the remaining 44. Find the probability it is (i) a black card, (ii) a jack. [CBSE] Solution: total 44. (i) black cards left $=26-4=22$: $\dfrac{22}{44}=\dfrac12$; (ii) jacks $=4$: $\dfrac{4}{44}=\dfrac1{11}$. Answers: $\dfrac12,\ \dfrac1{11}$.

PYQ 12 (3 marks): A bag contains balls numbered 1 to 20. One ball is drawn. Find the probability of a number that is (i) a multiple of 3, (ii) a perfect square. [CBSE] Solution: (i) $3,6,9,12,15,18$ → 6 → $\dfrac{6}{20}=\dfrac3{10}$; (ii) $1,4,9,16$ → 4 → $\dfrac{4}{20}=\dfrac15$. Answers: $\dfrac3{10},\ \dfrac15$.

PYQ 13 (2 marks): A die is thrown. Find the probability of getting a number greater than 4. [CBSE] Solution: $\{5,6\}$: $\dfrac26=\dfrac13$. Answer: $\dfrac13$.

PYQ 14 (3 marks): From a deck of 52, find the probability of drawing (i) a red king, (ii) a queen of black colour, (iii) a spade or an ace. [CBSE] Solution: (i) $\dfrac{2}{52}=\dfrac1{26}$; (ii) 2 black queens → $\dfrac{2}{52}=\dfrac1{26}$; (iii) 13 spades + 3 other aces $=16$ → $\dfrac{16}{52}=\dfrac4{13}$. Answers: $\dfrac1{26},\ \dfrac1{26},\ \dfrac4{13}$.

PYQ 15 (1 mark): Two coins are tossed. The probability of getting two tails is: (A) $\dfrac12$ (B) $\dfrac14$ (C) $\dfrac34$ (D) 1. [CBSE] Solution: only $TT$: $\dfrac14$. Answer: (B).

PYQ 16 (3 marks): A jar contains 24 marbles, some green and others blue. If the probability of drawing a green marble is $\dfrac23$, find the number of blue marbles. [CBSE] Solution: green $=\dfrac23\times24=16$; blue $=24-16=8$. Answer: 8 blue marbles.

PYQ 17 (3 marks): A game consists of spinning a wheel with 8 equal sectors numbered 1 to 8. Find the probability of getting (i) an even number, (ii) a number greater than 6. [CBSE] Solution: (i) $\{2,4,6,8\}$: $\dfrac{4}{8}=\dfrac12$; (ii) $\{7,8\}$: $\dfrac{2}{8}=\dfrac14$. Answers: $\dfrac12,\ \dfrac14$.

PYQ 18 (2 marks): A letter is chosen at random from the word "MATHEMATICS". Find the probability that it is the letter M. [CBSE] Solution: 11 letters, M appears twice: $\dfrac{2}{11}$. Answer: $\dfrac2{11}$.