## 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.

### What is the probability that the parcel was shipped express and arrived the next day?

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,….

### Given that the test is positive, what is the probability that the person has the disease?

1.  Refer to Exercise 28. Assume that both inspectors inspect every item and that if an item has no flaw, then neither inspector will detect a flaw. a.  Assume that….

### If a man tests negative, what is the probability that he actually has the disease?

1.  Refer to Example 2.26. a.  If a man tests negative, what is the probability that he actually has the disease? b.  For many medical tests, it is standard procedure….