Question

Consider a regular deck of cards with 52 cards in total. Four of a kind is a poker hand that contains all four cards of one rank and any other (unmatched) card. A full house is a hand that contains three matching cards of one rank and two matching cards of another rank. In a poker hand, are getting a "four of a kind" and getting a "full house" mutually exclusive events? Justify your answer.

Answer 1

Answer:

No.

Step-by-step explanation:

This is because if one event happens before the other, the odds of the other event happening will change due to less cards being left to pick from.

Consider the scenario where 4 of a kind all contained 10's from the deck.

The possibility of a full-house with a 10 in the pile would be zero if there were no 10's left after the four of a kind turn had been made. Thus, since the four of a kind affects the probability of the full house, and vice versa, they are both dependent on each other and hence not exclusive events.