question 5. is my solution correct? if not what is? Thank you a. exactly one ace

Question

question 5. is my solution correct? if not what is? Thank you

a. exactly one ace; b. at least one ace? Problem 5 Five cards are dealt from a shuffled deck. What is the probability that the dealt hand contains exactly two aces, given that we know it contains at least one ace? Problem 6 The 52 cards in a shuffled deck are dealt equally among four players, call them A, B, C, and D. If A and B have exactly 7 spades, what is the probability that C has exactly 4 spades? Problem 7 There are 50 students in a class and the professor chooses 15 students at random. What is the

Explanation / Answer

5) Solution:

Probability of being dealt at least one ace could mean 1, 2, 3, or 4
aces. This is best calculated from 1 - Prob(no aces)

  
Prob(no aces) = C(48,5)/C(52,5) = 0.658842

Probability of at least one ace = 0.341158

Prob(2 aces|at least one ace) = C(4,2) x C(48,3)/0.341158 x C(52,5)

= 0.11704

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