Question

In: Statistics and Probability

A standard deck of cards consists of four suits (clubs, diamonds, hearts, and spades), with each...

A standard deck of cards consists of four suits (clubs, diamonds, hearts, and spades), with each suit containing 13 cards (ace, two through ten, jack, queen, and king) for a total of 52 cards in all.

a.) How many 7-card hands will consist of exactly 3 kings and 2 queens?


b.) What is the probability of getting a 7-card hand that consists of exactly 3 kings and 2 queens? (Note: Enter your answer as a fraction.)

Solutions

Expert Solution

Number of kings in a deck of cards =4

Number of queens in a deck of cards = 4

Number of cards others than kings and queens = 52 - 4 - 4 = 52-8=44

Number of cards in a hand = 7

a)

Number of 7-card hands will consist of exactly 3 kings and 2 queens (other two cards are to be other than king and queen)

= Number of ways of getting 3 kings from 4 kings x

Number of ways of getting 2 queens from 4 queens x

Number of ways getting 2 cards other than kings and queens from 44 cards other than kings and queens

=

Number of 7-card hands will consist of exactly 3 kings and 2 queens = 22704

b)

Probability of getting a 7-card hand that consists of exactly 3 kings and 2 queens

= Number of 7-card hands will consist of exactly 3 kings and 2 queens / Number of 7-card hands

Number of 7-card hands = Number of ways of getting 7 cards from 52 cards =

From (a)

Number of 7-card hands will consist of exactly 3 kings and 2 queens = 22704

Probability of getting a 7-card hand that consists of exactly 3 kings and 2 queens

= Number of 7-card hands will consist of exactly 3 kings and 2 queens / Number of 7-card hands

=22704/133784560 = 1419/8361535

Probability of getting a 7-card hand that consists of exactly 3 kings and 2 queens

orchestra answered 2 years ago
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