1. Roll a pair of dice (one is red and the other is green). Let Abe the event that the red die is 4 or 5. Let B be the event thatthe green die is 1 Let C be the event that the dice sum is 7 or8.

1. Calculate P(A), P(B), P(C)
2. Calculate P(A|C), P(A|B)
3. Are the events A and C independent?

1. Suppose box 1 has four black marbles and two white marbles, andbox 2 has two black marbles and five marbles. If you picked onemarble from one of the two boxes at random, what it the probabilitythat you picked from box 1 given that the marble you picked isblack?

1. A raffle has 5000 tickets with the following prizes: 1 tickethas $2000 prize, 10 tickets have $200 prize, and 20 tickets have$50 prize and 500 tickets have a $20 prize. If to buy a ticketcosts $15, and X is the random variable that measures netprofit:

1. Calculate the pdf table of X
2. Calculate E(X), Var(X)

1. If a fair coin is flipped 120 times, what is the probabilitythat:

1. The number of heads is more than 70
2. The number of heads between 50 and 70?

1. According to a study, 21.1% of 507 female college students wereon a diet at the time of the study.

a) Construct a 99% confidence intervalfor the true proportion of all female students who were on a dietat the time of this study.

b) Explain what this intervalmeans.

c) Is it reasonable to think that only17% of college women are on a diet?

                                                                                                                                      

1. A used car dealer says that the mean price of a 2008 Honda CR-Vis at least $20,500. You suspect this claim is incorrect and findthat a random sample of 14 similar vehicles has a mean price of$19,850 and a standard deviation of $1084. Is there enough evidenceto reject the dealer’s claim at α = 0.05?