1. In a lot of n components, 30% are defective. Two components are drawn at random and tested. Let A be the event that the first component drawn is defective,….

## Which sequence is more likely, HTTHH or HHHHH? Or are they equally likely?

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.