Question

The probability of drawing a heart from a standard deck of 52 playing cards is 1 4 . The probability of drawing a face card from a standard deck of 52 playing cards is 3 13 . Based on this, Drew determines that the probability of drawing a heart face card is 3 52 . Is this correct? A) Yes, Drawing a heart and drawing a face card are independent events, so P(H ∩ F) = P(H)·P(F) = 1 4 · 3 13 = 3 52 . B) No, Drawing a heart and drawing a face card are independent events, so P(H U F) = P(H) + P(F) = 1 4 + 3 13 = 25 52 . C) No, Drawing a heart and drawing a face card are independent events, so P(H U F) = P(H) + P(F) - P(H ∩ F) = 1 4 + 3 13 - 3 52 = 11 26 . D) No, Drawing a heart and drawing a face card are dependent events, so the P(H ∩ F) = P(H)·P(F|H) = 1 4 · 3 52 + 1 4 · 2 51 = 5 204 .

Answer 1

We need Probability of drawing a heart Or drawing a face card other than a heart. 

This is 1/4 + 9/52  = 11/26
C is the correct choice.

Answer 2

A) Yes, Drawing a heart and drawing a face card are independent events, so P(H ∩ F) = P(H)·P(F) = 1 4 · 3 13 = 3 52