Two cards are drawn from a standard deck of cards.
Part A: If they are drawn with replacement, what is the probability that both cards are 2s? Show your work.
Part B: If they are drawn without replacement, what is the probability that the first card is a club and the second card is a spade? Show your work.
Part C: Which of the two scenarios in Part A or Part B represents dependent events? Explain your answer using complete sentences. Show your work.
A ....since we can replace the cards....the probability that that they are both 2's is just
(4/52) * (4/52) = 1/13 * 1/13 = 1/169
B......we are drawing without replacing....
First card a club / Second card a spade (given that the first card is a club) =
(13/52) (13/51) = (1/4) * (13/51) = 13 / 204
C The second is the dependent event . We have the same probability for drawing a 2 both times when we replace the cards. But without replacement, the probability on the second draw can be different. For instance.....if we draw a spade on the frist draw....the probability of drawing a spade on the second draw would be different = 12/51 = 4/13. So the second draw probability depends on the first draw.