Question

If two cards are randomly chosen from a standard deck, what is the probability that a 6 is chosen, NOT replaced, and another 6 is chosen?
A. 2/36
B. 16/2652
C. 16/2704
D. 12/2652

Answer 1

The probability of choosing a 6 without replacement is different from that of choosing a 6 with replacement.

First draw: P(6) = 4/52 = 1/4 (there are 4 6's in the full deck)

Second draw: P(6|6 was previously chosen and not replaced) = 4/51 (there are 3-6's left among 51 cards)

P(a 6 is chosen, NOT replaced, and another 6 is chosen) =

(1/4)(3/51) = 1/68

Answer 2

$|\Omega|=52\cdot51=2652\\ |A|=4\cdot3=12\\\\ P(A)=\dfrac{12}{2652}\Rightarrow \text{D}$