CBSE Class 10 Mathematics Probability Worksheet Set D

1. Probability–A Theoretical Approach

In theoretical approach of probability, predictions about the happenings, on the basis of certain assumptions, are made without actually performing the experiment. Probability of an event E is defined as P(E) and is given by the formula: \[ P(E) = \frac{\text{Number of trials in which the event happened}}{\text{Total number of trials}} \]

Question. A card is drawn from a deck of 52 cards. The event E is that the card is not an ace of hearts. The number of outcomes favourable to E is
(a) 52
(b) 53
(c) 51
(d) 31
Answer: (c) 51

Question. A card is selected from a deck of 52 cards. The probability of it being a red face card is
(a) \( \frac{5}{52} \)
(b) \( \frac{7}{52} \)
(c) \( \frac{3}{26} \)
(d) \( \frac{5}{26} \)
Answer: (c) \( \frac{3}{26} \)

Question. A card is drawn at random from a well-shuffled pack of 52 playing cards. The probability of getting neither a red card nor a queen is
(a) \( \frac{6}{13} \)
(b) \( \frac{7}{13} \)
(c) \( \frac{11}{13} \)
(d) \( \frac{9}{13} \)
Answer: (a) \( \frac{6}{13} \)

Question. Two dice are thrown at the same time and the product of numbers appearing on them is noted. The probability that the product is a prime number is
(a) \( \frac{1}{3} \)
(b) \( \frac{1}{6} \)
(c) \( \frac{1}{5} \)
(d) \( \frac{5}{6} \)
Answer: (b) \( \frac{1}{6} \)

Question. Rahim tosses two different coins simultaneously. The probability of getting at least one tail is
(a) \( \frac{1}{4} \)
(b) \( \frac{3}{4} \)
(c) \( \frac{3}{5} \)
(d) \( \frac{1}{6} \)
Answer: (b) \( \frac{3}{4} \)

Question. A jar contains 24 marbles, some are green and other are blue. If a marble is drawn at random from the jar, the probability that it is green is \( \frac{2}{3} \). The number of blue marbles in the jar is
(a) 5
(b) 6
(c) 4
(d) 8
Answer: (d) 8

Question. A game consists of tossing a 10 rupee coin 3 times and noting its outcome each time. Sudhir wins if all the tosses give the same result, i.e., three heads or three tails and loses otherwise. The probability that Sudhir will not win the game is
(a) \( \frac{1}{4} \)
(b) \( \frac{1}{6} \)
(c) \( \frac{3}{4} \)
(d) 10
Answer: (c) \( \frac{3}{4} \)

Question. In the given figure, a disc is shown on which a player spins arrow twice. The fraction \( \frac{a}{b} \) is formed, where ‘a’ is the number of sector on which arrow stops in the first spin and ‘b’ is the number of the sector in which the arrow stops in the second spin. On each spin, each sector has equal chance of selection by the arrow. The probability that the fraction \( \frac{a}{b} > 1 \) is
(a) \( \frac{1}{12} \)
(b) \( \frac{5}{6} \)
(c) \( \frac{5}{12} \)
(d) 1
Answer: (c) \( \frac{5}{12} \)

Exercise 8.1

Question. One card is drawn from a well shuffled deck of 52 cards. The probability that it is black queen is
(a) \( \frac{1}{26} \)
(b) \( \frac{1}{13} \)
(c) \( \frac{1}{52} \)
(d) \( \frac{2}{13} \)
Answer: (a) \( \frac{1}{26} \)

Question. The probability of an impossible event is
(a) 1
(b) \( \frac{1}{2} \)
(c) not defined
(d) 0
Answer: (d) 0

Question. If P(A) denotes the probability of an event A, then
(a) P(A) < 0
(b) P(A) > 1
(c) 0 ≤ P(A) ≤ 1
(d) –1 ≤ P(A) ≤ 1
Answer: (c) 0 ≤ P(A) ≤ 1

Question. If the probability of an event is p, the probability of its complementary event will be
(a) p – 1
(b) p
(c) 1 – p
(d) \( 1 - \frac{1}{p} \)
Answer: (c) 1 – p

Question. Someone is asked to take a number from 1 to 100. The probability that it is a prime is
(a) \( \frac{1}{5} \)
(b) \( \frac{6}{25} \)
(c) \( \frac{1}{4} \)
(d) \( \frac{13}{15} \)
Answer: (c) \( \frac{1}{4} \)

Question. A number is chosen at random from the numbers –5, –4, –3, –2, –1, 0, 1, 2, 3, 4, 5. Then the probability that square of this number is less than or equal to 1 is
(a) \( \frac{1}{11} \)
(b) \( \frac{2}{11} \)
(c) \( \frac{3}{11} \)
(d) \( \frac{3}{26} \)
Answer: (c) \( \frac{3}{11} \)

Question. If the probability of an event E happening is 0.023, then \( P(\bar{E}) = \)
(a) 0.245
(b) 0.977
(c) 0.678
(d) 0.5
Answer: (b) 0.977

Question. A card is drawn at random from a well shuffled pack of 52 playing cards. The probability of getting a red face card is
(a) \( \frac{3}{26} \)
(b) \( \frac{5}{26} \)
(c) \( \frac{2}{13} \)
(d) \( \frac{1}{26} \)
Answer: (a) \( \frac{3}{26} \)

Question. A die is thrown once. What is the probability of getting a number greater than 4?
(a) \( \frac{1}{2} \)
(b) \( \frac{1}{3} \)
(c) \( \frac{1}{4} \)
(d) \( \frac{1}{5} \)
Answer: (b) \( \frac{1}{3} \)

Question. Two different dice are tossed together. The probability that the product of the two numbers on the top of the dice is 6 is
(a) \( \frac{4}{9} \)
(b) \( \frac{5}{9} \)
(c) \( \frac{8}{9} \)
(d) \( \frac{1}{9} \)
Answer: (d) \( \frac{1}{9} \)

Question. A number is chosen at random from the numbers −3, −2, −1, 0, 1, 2, 3. What will be the probability that square of this number is less than or equal to 1?
(a) \( \frac{3}{7} \)
(b) \( \frac{4}{7} \)
(c) \( \frac{5}{7} \)
(d) \( \frac{6}{7} \)
Answer: (a) \( \frac{3}{7} \)

Question. A letter of English alphabet is chosen at random. The probability that the chosen letter is a consonant is
(a) \( \frac{7}{26} \)
(b) \( \frac{5}{26} \)
(c) \( \frac{11}{26} \)
(d) \( \frac{21}{26} \)
Answer: (d) \( \frac{21}{26} \)

Question. A die is thrown once. What is the probability of getting a number less than 3?
(a) \( \frac{1}{2} \)
(b) \( \frac{1}{3} \)
(c) \( \frac{1}{5} \)
(d) \( \frac{1}{9} \)
Answer: (b) \( \frac{1}{3} \)

Question. If the probability of winning a game is 0.07, what is the probability of losing it?
(a) 0.33
(b) 0.63
(c) 0.93
(d) 0.57
Answer: (c) 0.93

Question. The probability of getting a doublet in a throw of a pair of dice is
(a) \( \frac{1}{2} \)
(b) \( \frac{1}{4} \)
(c) \( \frac{1}{5} \)
(d) \( \frac{1}{6} \)
Answer: (d) \( \frac{1}{6} \)

Question. The probability of getting a black queen when a card is drawn at random from a well-shuffled pack of 52 cards is
(a) \( \frac{1}{26} \)
(b) \( \frac{3}{26} \)
(c) \( \frac{8}{13} \)
(d) 1
Answer: (a) \( \frac{1}{26} \)

Question. A game consists of tossing a coin 3 times and noting the outcomes each time. If getting the same result in all the tosses is a success, the probability of losing the game is
(a) \( \frac{3}{4} \)
(b) \( \frac{1}{4} \)
(c) \( \frac{3}{8} \)
(d) 1
Answer: (a) \( \frac{3}{4} \)

Question. A ticket is drawn at random from a bag containing tickets numbered from 1 to 40. The probability that the selected ticket has a number which is a multiple of 5 is
(a) \( \frac{1}{5} \)
(b) \( \frac{3}{5} \)
(c) \( \frac{4}{5} \)
(d) 1
Answer: (a) \( \frac{1}{5} \)

Question. The king, queen and jack of clubs are removed from a deck of 52 playing cards and the remaining cards are shuffled. A card is drawn from the remaining cards. The probability of getting a card of queen is
(a) \( \frac{1}{49} \)
(b) \( \frac{2}{49} \)
(c) \( \frac{3}{49} \)
(d) \( \frac{5}{49} \)
Answer: (c) \( \frac{3}{49} \)

Question. A coin is tossed two times. Find the probability of getting at least one head is
(a) \( \frac{1}{4} \)
(b) \( \frac{3}{4} \)
(c) \( \frac{1}{8} \)
(d) \( \frac{3}{8} \)
Answer: (b) \( \frac{3}{4} \)

Question. The probability of guessing the correct answer to a certain test is \( \frac{p}{12} \). If the probability of not guessing the correct answer to this question is \( \frac{1}{3} \), then the value of p is
(a) 2
(b) 4
(c) 6
(d) 8
Answer: (d) 8

Question. If a number x is chosen at random from the numbers –3, –2, –1, 0, 1, 2, 3. What is probability that \( x^2 \le 4 \)?
(a) \( \frac{5}{7} \)
(b) \( \frac{3}{7} \)
(c) \( \frac{4}{7} \)
(d) \( \frac{6}{7} \)
Answer: (a) \( \frac{5}{7} \)

Question. A letter is selected at random from the set of English alphabets. What is the probability that it is a vowel?
(a) \( \frac{1}{26} \)
(b) \( \frac{3}{26} \)
(c) \( \frac{5}{26} \)
(d) \( \frac{7}{26} \)
Answer: (c) \( \frac{5}{26} \)

B. Assertion-Reason Type Questions

Question. Assertion (A): If a pair of dice is thrown once, then the probability of getting a sum of 8 is \( \frac{5}{36} \).
Reason (R): In a simultaneous toss of two coins, the probability of getting exactly one head is \( \frac{1}{2} \).
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true.
Answer: (b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).

Question. Assertion (A): The probability of a sure event is 1.
Reason (R): Let E be an event. Then 0 ≤ P (E) ≤ 1.
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion

Case Study Based Questions

Some boys are playing with numbers. There is a box which contains 90 discs. They are numbered from 1 to 90. The boys are drawing disc one by one from the box at random and want to find the probability of a particular number.

Question. If one disc is drawn at random from the box, the probability that it bears a two-digit number is
(a) \( \frac{9}{10} \)
(b) \( \frac{8}{90} \)
(c) \( \frac{89}{90} \)
(d) \( \frac{79}{90} \)
Answer: (a) \( \frac{9}{10} \)

Question. Then they put the disc into the box and draw another disc at random. They want to know the probability that it bears a perfect square number. So, the probability of perfect square number is
(a) \( \frac{8}{90} \)
(b) \( \frac{3}{10} \)
(c) \( \frac{1}{10} \)
(d) \( \frac{1}{9} \)
Answer: (c) \( \frac{1}{10} \)

Question. They put the disc into the box and another boy draws another disc at random, and wants to know the probability that it bears a number divisible by 5. So the probability is
(a) \( \frac{2}{5} \)
(b) \( \frac{3}{5} \)
(c) \( \frac{4}{5} \)
(d) \( \frac{1}{5} \)
Answer: (d) \( \frac{1}{5} \)

Question. After putting the disc into the box, the next boy draws a disc at random and wants to know the probability that it bears a prime number. The probability is
(a) \( \frac{5}{18} \)
(b) \( \frac{4}{15} \)
(c) \( \frac{2}{15} \)
(d) \( \frac{13}{45} \)
Answer: (c) \( \frac{2}{15} \)

Question. The boys put all the disc together into the box and next boy draws a disc at random and find the probability that the disc bears a number divisible by 7.
(a) \( \frac{1}{15} \)
(b) \( \frac{2}{15} \)
(c) \( \frac{4}{15} \)
(d) \( \frac{1}{5} \)
Answer: (b) \( \frac{2}{15} \)