Question

Three cards are dealt from a deck of 52 playing cards. Find the probability that a 3 card hand consists of: a. All hearts ( Answer is P(13,3)) b. An Ace, King and Queen of the same suit (Answer is P(4)) c. A pair of 2s (Answer is C(4,2) x C(48,1) Need help setting up the problem

Answer 1

Number of suits in a deck = 4

Number of card for each suit = 13

Total cards = 52

a) Probability that the 3 cards are all heart =

= P(13,3) / P(52,3)

= (13!/10!) / (52!/49!)  

= 0.0129

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b) Probability that the 3 cards are Ace, King and Queen of the same suit(there are 4 suit in a deck) =  

= 1 / 4

= 0.25

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c) There are total four 2s in a deck, 1 in each suit.

and the 3rd card will be choose from the remaining 52-4 =48 cards

Probability of a pair of 2's = (C(4, 2)*C(48,1))/ (C(52, 3)

= (4!/(2!*2!))*(48!/(47!*1!)) / (52!/(3!*49!))

= 0.0130