(Question 1) Multiple Choice (15 pts) 1.A. (5 pts) You went to a casino to play
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(Question 1) Multiple Choice (15 pts) 1.A. (5 pts) You went to a casino to play Texas holdem poker. The dealer gives you 5 cards from a deck of 52 cards. What is the probability that you will get 3 of a kind (e.g., get 3 Aces and 2 random cards, get 3 tens and 2 random cards, etc.) 1.B. (5 pts) Assume you have an urn with 10 cards. Eight of those cards are red and the remaining two cards are black. You picked three cards one after the other at random without replacement. What is the probability that you will get two consecutive red cards? 1.C. (5 pts) There are three sections of IMSE 317 and you have 4 of your friends taking the course. What is the probability that you will end up enrolling in the same section with at least one of them?Explanation / Answer
A) total kard =52
three of a kind = 13C1·4C3·12C2·4C1·4C1
= 13·4·66·4·4
= 54,912
Total possibilities for 5 cards =52C5 = 2998960
P(three of a kind) = 54,912 /2998960 = 0.021128
B)
N=Total cards=10
r=Red card2 =8
Black cards =2
n=3
x=2
Using hyper geomtric distribution
=HYPGEOM.DIST(2,3,8,10,0)
=0.466667
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