Question

1. A five-card poker hand is dealt from a standard deck of
cards. Find the probability that:

a. The hand contains exactly 3 Clubs and exactly 1
Spade.

b. The hand contains at least two aces

c. The hand contains all cards from the same suit

d. The hand contains three cards from one suit and two cards
from different suit

e. The hand contains no more than one spade

Answer #1

5 cards out of 52 can be chosen in ways.

a) P[Exactly 3 clubs and 1 spade] = [ 3 clubs from 13 , 1 spade from 13 , 1 from 26 non club non spade cards]

b) P[ No aces] =

and P[ exactly one ace] =

SO, P[At least 2 aces] = 1- P[no ace] - P[exactly one ace ] = 1- 0.6588-0.2995 = 0.0417

c) P[All from same suit] = [ 4 different suits, choose 1 , and then choose 5 cards of 13 cards of that suit]

d) P[[3 from one suit 2 from different suit ] =

e) P[ no spade ] =

P[ exactly one spade] =

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