Many variants of poker are played with both cards in players’ hands and shared community cards. Players’ hand are some combination of the two sets of cards. For parts (a) and (b), consider playing such that Anna, Brad, Charlie, and Dre each have 2 cards for themselves, and build a 5 card hand out of those 2 cards and 3 shared cards. Assume a standard 52-card deck is being used.

(a) What is the probability that Anna has a flush, where her 2 cards and the 3 community cards share a suit?
(b) What is the probability that Brad also has a flush given that Anna has a flush?
(c) Suppose for the next round, when the cards are dealt a 4th community card is added to the center, and play. What is the probability that Charlie has a flush? For this variant, a flush means at least 5 of the 6 cards a player has access to - in their hand or the community - share a suit.
(d) For this round in part (c) with a 4th community card, what is the probability that Dre also has a flush given that Charlie has a flush?