71. Four red cards (i.e., hearts and diamonds) and four black cards are face down on thetable. A psychic who claims to be able to locate the four black cards turns over 4 cards andgets 3 black cards and 1 red card. What is the probability he would get 3 or 4 black cardsif he were guessing? Chapter 3 5. Two people, whom we call South and North, draw 13 cards out of a deck of 52. Southhas two Aces. What is the probability that North has (a) none? (b) one? (c) the other two?South has 2 aces and 11 non-aces leaving 2 aces and 37 nonaces in the deck. (a) 11. Brown eyes are dominant over blue. That is, there are two allelesBandb.bbindividualshave blue eyes but other combinations has brown eyes. Your parents and you have brown eyesbut your brother has blue. So you can infer that both of your parents are heterozygotes, i.e.,have genetic typeBb. Given this information what is the probability you are a homozygote. 13. Two events haveP(A) = 1/4,P(B|A) = 1/2, andP(A|B) = 1/3. ComputeP(A∩B),P(B),P(A∪B). 15. From a signpost that says MIAMI two letters fall off. A friendly drunk puts the twoletters back into the two empty slots at random. What is the probability that the sign stillsays MIAMI? 20. In a dice game the “dealer” rolls two dice, the player rolls two dice, and the player winsif his total is larger (>) than the dealer’s. What is the probability the player wins? 4
2 28. Suppose that the number of children in a family has the following distributionnumber of children01234probability0.150.250.30.20.1Assume that each child is independently a girl or a boy with probability 1/2 each. If a familyis picked at random what is the chance it has exactly two girls.
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- Probability, Probability theory