Class 10 - Chapter 14: Probability

Section A (1 Mark each)

Q1. Two dice are thrown simultaneously. The probability of getting a doublet is:

(a) $\frac{1}{3}$ (b) $\frac{1}{6}$ (c) $\frac{1}{4}$ (d) $\frac{2}{3}$

Q2. A card is drawn from a well shuffled deck of 52 cards. The probability of getting a black face card is:

(a) $\frac{3}{26}$ (b) $\frac{3}{13}$ (c) $\frac{3}{52}$ (d) $\frac{1}{26}$

Q3. Which of the following is the probability of getting a sum of 7 when two dice are thrown?

(a) $\frac{1}{6}$ (b) $\frac{1}{12}$ (c) $\frac{5}{36}$ (d) $\frac{7}{36}$

Q4. Assertion (A): The probability of drawing a red card from a deck of 52 cards is $\frac{1}{2}$.
Reason (R): There are 26 red cards (Hearts and Diamonds) in a standard deck.

(a) Both A and R are true and R is the correct explanation of A. (b) Both A and R are true but R is not the correct explanation of A. (c) A is true but R is false. (d) A is false but R is true.

Section B (2 Marks each)

Q5. Two dice are thrown together. Find the probability that the sum of the numbers on the top of the dice is (i) 9 (ii) 12.

Solve on white paper.

Q6. A card is drawn at random from a well-shuffled pack of 52 playing cards. Find the probability of getting (i) a red king (ii) a queen or a jack.

Solve on white paper.

Q7. A die is thrown twice. What is the probability that (i) 5 will not come up either time? (ii) 5 will come up at least once?

Solve on white paper.

Section C (3 Marks each)

Q8. 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 a:
(i) face card
(ii) red card
(iii) black card

Solve on white paper.

Q9. Two dice are thrown simultaneously. Find the probability that the product of the numbers appearing on the top of the dice is:
(i) 6
(ii) 12
(iii) 7

Solve on white paper.

Section D (5 Marks)

Q10. The King, Queen and Jack of clubs are removed from a deck of 52 playing cards and then well shuffled. One card is selected from the remaining cards. Find the probability of getting:
(i) a heart
(ii) a king
(iii) a club
(iv) the '10' of hearts
(v) a face card

Solve on white paper.

Section E (4 Marks)

Q11. Case Study: Dice Game

Two friends, Rahul and Ravi, are playing a game with two dice. They agree that if the sum of numbers is a prime number, Rahul wins. If the sum is a composite number, Ravi wins.

(i) List all outcomes where the sum is a prime number.

(ii) Find the probability that Rahul wins.

(iii) Find the probability that Ravi wins.

Solve on white paper.