A 5-card hand is dealt from a deck of 52 cards. What is the probability that a) none are queens?
b) all are queens?

A) a) $0.07487$
b) 0

B) a) 0
b) $0.07487$

C) a) $0.65884$
b) 0

D) a) 0 b)
$0.65884$

Question

A 5-card hand is dealt from a deck of 52 cards. What is the probability that a) none are queens?
b) all are queens?

A) a) $0.07487$
b) 0

B) a) 0
b) $0.07487$

C) a) $0.65884$ 
b) 0

D) a) 0 b) 
$0.65884$

Quizplus · Accepted Answer

a) To find the probability that none are queens, we calculate the probability of selecting 5 cards out of the 48 that are not queens (since there are 4 queens in a 52-card deck). This is $\frac{{48 \choose 5}}{{52 \choose 5}} \approx 0.65884$.b) The probability that all 5 cards are queens is the probability of selecting the 4 queens out of 4 and 1 card out of the remaining 48, which is 0 because you cannot select 5 queens from a set of only 4 queens in a standard deck.

A 5-Card Hand Is Dealt from a Deck of 52 0.074870.074870.07487

A 5-Card Hand Is Dealt from a Deck of 52 $0.07487$