Euchre is a card game that uses a 24card deck which can be f

Euchre is a card game that uses a 24-card deck (which can be formed by removing all of the 2’s, 3’s, 4’s, 5’s, 6’s, 7’s, and 8’s from a standard 52-card deck) in which the players are each dealt 5-card hands from the deck of 24. Suppose that you are playing Euchre and are dealt a 5-card hand.

A. What is the probability that you are dealt no more than 1 queen?

B. What is the probability that you are dealt no aces and exactly 2 hearts?

Solution

After removing 2’s, 3’s, 4’s, 5’s, 6’s, 7’s, and 8’s, remaining cards = 24

Out of this no of queens = 4

Prob for 1 queen = 4/24 = 1/6

X- no of queens is binomial with p = 0.1667 and n = 5

A) Prob (Queen <=1) = 0.8037

B)

Prob (no ace and 2 hearts)

= Prob of 2 hearts from 20 cards excluding aces

Y - no of hearts is binomial with p = 4/20 = 1/5 and n = 5

P(Y=0) = 0.2048

=