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 10s? Show your work. (1 point)
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 diamond? Show your work. (1 point)
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. (2 points)
We have 4 10s......so if we have replacement....the probability of drawing a 10 on each draw is the same = 4/52
P (Two 10s with replacement) = 4/52 * 4/52 = 1/13 * 1/13 = 1/169
B ) Without replacement we have 4/52 of drawing a 10 on the first draw and (3/51) of drawing a 10 on the second draw
So.....this probability = 4/52 * 3/51 = (1/13) * (1/17) = 1/ 221
C) The second event is dependent. If we don't draw a 10 on the first draw, the probability of drawing a 10 on the second draw is different = 4/ 51. In the first scenario, the probability of drawing a 10 is the same on both draws. Thus, it is independent - one draw does not affect the other.