Question

Petra draws two cards from a standard 52-card deck. Does Petra have a greater probability of drawing two hearts if the she replaces the first card before the second draw, or if she does not replace the first card? Justify your answer using numbers and words.

Answer 1

She has a higher probability if she replaces the card before drawing the second one.

The probability of drawing a heart the first time is 13/52. If she replaces the card, the probability of drawing a second heart would again be 13/52;

13/52(13/52) = 169/2704 = 0.0625.

However, if she does not replace it, the probability of drawing a second heart would be 12/52;

13/52(12/51) = 156/2652 = 0.0588.

The probability is higher with replacement.