## What is the smallest possible value for Y?

1.   Candidates for a job are interviewed one by one until a qualified candidate is found. Thirty percent of the candidates are qualified.

a.  What is the probability that the first candidate is qualified?

b.  What is the probability that the first candidate is unqualified and the second candidate is qualified?

c.   Let X represent the number of candidates interviewed up to and including the first qualified candidate.

d.  Find P(X = 4). Find the probability mass function of X.

2.   Refer to Exercise 10. The company has two positions open. They will interview candidates until two qualified candidates are found. Let Y be the number of candidates interviewed up to and including the second qualified candidate.

a.  What is the smallest possible value for Y?

b.  What is the probability that Y takes on that value?

c.   Let X represent the number of applicants who are interviewed up to and including the first qualified candidate.

d.  Find P(Y = 4 ∣ X = 1).

e.  Find P(Y = 4 ∣ X = 2).

f.    Find P(Y = 4).

### 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….