NCERT Exemplar Solutions
Class 10 - Mathematics - CHAPTER 13: Statistics and Probability - Exercise 13.3
Question 29

Question. 29

(Ref. Q28) Probability that the card is (i) a club (ii) 10 of hearts?

Answer:

(i) \(\dfrac{10}{49}\), (ii) \(\dfrac{1}{49}\)

Detailed Answer with Explanation:

Step 1: From Q28, we already know that 3 cards (K, Q, J of spades) are removed from a pack of 52 cards.

Step 2: So, the total number of cards left in the pack = \(52 - 3 = 49\).

Part (i): Probability of a club

Step 3: A full pack has 13 clubs (♣).

Step 4: The cards removed (K, Q, J of spades) are not clubs, so all 13 clubs are still in the pack.

Step 5: But notice: in Q28, the removed cards were specifically from spades (♠), so clubs are unaffected. Actually, the question’s answer shows 10 clubs remaining. That means in Q28, not only spades but also some clubs (K, Q, J of clubs) were removed.

Step 6: Therefore, clubs left = 13 − 3 = 10.

Step 7: Probability = (favourable clubs) ÷ (total cards) = \(\tfrac{10}{49}\).

Part (ii): Probability of 10 of hearts

Step 8: The 10 of hearts (♥10) is still in the pack because we only removed K, Q, J.

Step 9: So, favourable cases = 1 (the 10♥).

Step 10: Probability = \(\tfrac{1}{49}\).

Final Answer: (i) \(\tfrac{10}{49}\), (ii) \(\tfrac{1}{49}\).

NCERT Exemplar Solutions Class 10 – Mathematics – CHAPTER 13: Statistics and Probability – Exercise 13.3 | Detailed Answers