Question

Three cards are drawn at random without replacement from a standard deck of 52 playing cards. Find the probability that the second card is a spade, given that the first card was black.

Answer 1

2 cases:

1 - the first card was a spade, then a spade, then anything:
prob(your event) = (13/52)(12/51)(50/50) = 1/17 ----- there are only 12 spades left
2 - the first card was a club, then a spade, then anything
prob(of that event) = (13/52)(13/51)(50/50) = 13/204 --- all 13 spades are still there

Prob(event as stated) = 1/17 + 13/204 = 25/204