NCERT Exemplar Solutions
Class 10 - Mathematics - CHAPTER 13: Statistics and Probability - Exercise 13.1
Question 18

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).

NCERT Exemplar Solutions Class 10 – Mathematics – CHAPTER 13: Statistics and Probability – Exercise 13.1 | Detailed Answers