Question

What is the probability of getting a red numbered card greater than 6 from a well shuffled deck of 52 cards?

• A. \(4/13 \)
• B. \(2/13 \)
• C. \(5/13 \)
• D. \(3/13 \)

Hint:

Remember: "Greater than 6" does not include the 6 itself, and "Numbered cards" do \textbfnot include Aces, Kings, Queens, or Jacks.

Answer 1

The Correct Option is B

Concept: Probability \(P(E)\) is defined as: \[ P(E) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \] A standard deck of 52 cards has 26 red cards (Hearts and Diamonds). Numbered cards in each suit range from 2 to 10.
Step 1: Identify the favorable outcomes.
Numbered cards greater than 6 are: 7, 8, 9, and 10.
In red suits (Hearts and Diamonds), these are:
• Hearts: 7, 8, 9, 10 (4 cards)
• Diamonds: 7, 8, 9, 10 (4 cards) Total favorable cards = \(4 + 4 = 8\).

Step 2: Calculate the probability.
Total cards = 52. \[ P = \frac{8}{52} \] Divide both numerator and denominator by 4: \[ P = \frac{2}{13} \]