Question

1. You own n colors, and want to use them to color 6 objects. For each object, you randomly choose one of the colors. How large does n have to be so that odds are that no two objects will have the same color (i.e., every object is colored in a different color)? 2. Consider the following game: An urn contains 20 white balls and 10 black balls. If you draw a white ball, you get $1, but if you draw a black bal, you loose $2. (a) You draw 6 balls out of the urn. What is the probability that you will win money? (b) How many balls should you draw in order to maximize the probability of win- nng 3. Assume that the events E1, E2 are independent a) Prove that the events Ef, Es are also independent. b) If, in addition, P(E)and P(E2)Prve that c) If, in addition, Es is a third event that is independent of E and of E2, and such that P(E3)- . Prove that 19 24 17

Answer 1