Question

(a) 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

yes, getting a "four of a kind" and getting a "full house" are mutually exclusive events

Explanation:

Two mutually exclusive events are defined as events that have not intersection. In this case, it is imposible getting a "four of a kind" and getting a "full house" at the same time, so, intersection between this two events is void, with probablity zero, in conclusion, getting a "four of a kind" and getting a "full house" are mutually exclusive events.