Question:
What is the probability of getting a red numbered card greater than 6 from a well shuffled deck of 52 cards?
What is the probability of getting a red numbered card greater than 6 from a well shuffled deck of 52 cards?
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Remember: "Greater than 6" does not include the 6 itself, and "Numbered cards" do \textbfnot include Aces, Kings, Queens, or Jacks.
Updated On: Apr 1, 2026
- \(4/13 \)
- \(2/13 \)
- \(5/13 \)
- \(3/13 \)
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The Correct Option is B
Solution and Explanation
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: \[ P = \frac{2}{13} \]
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: \[ P = \frac{2}{13} \]
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