Question

Now suppose that you shuffle the deck thoroughly and deal a standard five-card hand without replacement. Give the probability that the hand:

(a) has only face cards (Jack, Queen, King);

(b) has only red cards and does not contain an Ace;

(c) is a Flush (all of one suit) containing only non-face cards;

(d) contains neither an even-numbered card (2,4,6,8,10) nor a Spade.

(e) contains at least one Ace and at least one Club.

Answer 1

The number of ways to deal a standard five-card hand without replacement = =  2,598,960.

a.) There are total 12 face cards ( 4 jack,4 queen ,4 king) .

The probability of getting only face cards = = 0.0003047373

b.) There are total 26 red cards including 2 aces,

the probability of getting only red cards and not containing an Ace = = 0.016354234

c.) Probability of all cards is a Flush (all of one suit) containing only non-face cards =

= 4x

= 0.0003878474

d.) There are 5 even numbered card in a suit and 13 spades.

Probability of getting neither an even-numbered card (2,4,6,8,10) nor a Spade

=

= 0.016354234

e.) There are 1 ace card in each suit and 13 clubs.

Probability of getting at least one Ace and at least one Club = 1 - no ace and no clubs.

= 1 - ( )

=.1 - 0.1450549451

= 0.8549450549