## What is the probability that none of the sample individuals carries the gene?

1.   A data center contains 1000 computer servers. Each server has probability 0.003 of failing on a given day.

a.   What is the probability that exactly two servers fail?

b.   What is the probability that fewer than 998 servers function?

c.    What is the mean number of servers that fail?

d.  What is the standard deviation of the number of servers that fail?

2.   One out of every 5000 individuals in a population carries a certain defective gene. A random sample of 1000 individuals is studied.

a.   What is the probability that exactly one of the sample individuals carries the gene?

b.   What is the probability that none of the sample individuals carries the gene?

c.   What is the probability that more than two of the sample individuals carry the gene?

d.  What is the mean of the number of sample individuals that carry the gene?

e.  What is the standard deviation of the number of sample individuals that carry the gene?

### 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….