1.  Refer to Exercise 23. Assume that the probabilities that each of the three scenarios occurs are P(A) = 0.20, P(B) = 0.30, and P(C) = 0.50.

a.   Find the probability that scenario A occurs and that the loss is 5%.

b.  Find the probability that the loss is 5%.

c.    Find the probability that scenario A occurs given that the loss is 5%.

2.  A box contains four 75 W lightbulbs, three 60 W lightbulbs, and three burned-out lightbulbs. Two bulbs are selected at random from the box. Let X represent the number of 75 W bulbs selected, and let Y represent the number of 60 W bulbs selected.

a.  Find the joint probability mass function of X and Y.

b.  Find µX .

c.    Find µY .

d.   Find σX .

e.   Find σY .

f.      Find Cov(X,Y).

g.   Find ρX,Y .

3.   A fair coin is tossed five times. Which sequence is more likely, HTTHH or HHHHH? Or are they equally likely? Explain.