Help! 1. (10 points) True or false. For two events A and B, AB’=(A’UB)’. Briefly

Question

Help!

1. (10 points) True or false. For two events A and B, AB’=(A’UB)’.   Briefly explain your answer, using pictures if necessary.

2.You are playing Texas Hold ‘em.   For your two card hand, you receive an Ace and a King. This is a good hand to start with, and there are many ways it can become a very good hand. (In particular, you can make three-of a kind, where the cards dealt on the board include two kings or two aces, making three total, including the ones in your hand.)

b) (10 points) What is the probability that there are exactly two kings dealt on the flop? That is, of the first three cards dealt to the table (not including the two in your hand) what is the probability that two exactly two kings are amongst the first three cards dealt?

c)(10 points) Suppose the answer to part a is .02, what is the probability that there are two kings or two aces on the flop?

Explanation / Answer

(1) For two events P and Q, we have DeMorgan's law which states that (P U Q)' = P' intersection Q'

Let P = A' and Q = B, then (A' U B)' = (A')' intersection B' = A intersection B'

The given statement is true.

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