A deck of 52 cards is mixed well, and 5 cards are dealt. (a) It can be shown tha

Question

A deck of 52 cards is mixed well, and 5 cards are dealt.

(a) It can be shown that (disregarding the order in which the cards are dealt) there are 2,598,960 possible hands, of which only 1287 are hands consisting entirely of spades.
What is the probability that a hand will consist entirely of spades? (Give the answer to six decimal places.)


What is the probability that a hand will consist entirely of a single suit? (Give the answer to six decimal places.)


(b) It can be shown that exactly 63,206 hands contain only hearts and diamonds, with both suits represented.
What is the probability that a hand consists entirely of hearts and diamonds with both suits represented? (Give the answer to five decimal places.)


(c) Using the result of Part (b), what is the probability that a hand contains cards from exactly two suits? (Give the answer to five decimal places.)

Explanation / Answer

Sol)

a) Total cases =2598960

Favourable cases=1287

What is the probability that a hand will consist entirely of spades is

1287/2598960= 4.951980792 x 10^-4

probability that a hand will consist entirely of a single suit is

1287 / ( 2598960*4) =0.00198

B)

shown that exactly 63,206 hands contain only hearts and diamonds

probability that a hand consists entirely of hearts and diamonds with both suits represented is

63206/2598960=.024320

C) The probability that a hand contains cards from exactly two suits is

6*(63206/2598960)=.145918

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