NCERT Exemplar Solutions
Class 10 - Mathematics - CHAPTER 13: Statistics and Probability - Exercise 13.1Question 18
Class 10 - Mathematics - CHAPTER 13: Statistics and Probability - Exercise 13.1
Question. 18
A card is selected from a deck of 52 cards. The probability that it is a red face card is
(A)
\(\dfrac{3}{26}\)
(B)
\(\dfrac{3}{13}\)
(C)
\(\dfrac{2}{13}\)
(D)
\(\dfrac{1}{2}\)
Detailed Answer with Explanation:
Step 1: A standard deck has 52 cards in total.
Step 2: The cards are divided into two colors:
- 26 red cards (Hearts ♥ and Diamonds ♦)
- 26 black cards (Clubs ♣ and Spades ♠)
Step 3: Face cards are Jack (J), Queen (Q), and King (K).
Step 4: Each suit (♥, ♦, ♣, ♠) has 3 face cards (J, Q, K).
Step 5: We only want red face cards. There are 2 red suits (♥ and ♦). So:
Number of red face cards = \(3 + 3 = 6\).
Step 6: Probability formula is:
\( P(E) = \dfrac{\text{Favourable outcomes}}{\text{Total outcomes}} \)
Here, favourable outcomes = 6, total outcomes = 52.
Step 7: So, \( P = \dfrac{6}{52} = \dfrac{3}{26} \).
Final Answer: Option (A).