STAT 301 - Business Statistics
Lecture Review #4 - Revising Probabilities

Review questions:

1) What are independent events? Dependent events? Mutually exclusive events. Give examples to illustrate.

2) What is meant by a conditional probability?

3) What is a false positive? A false negative?

4) What is Simpson’s Paradox? Give an example to illustrate.

Computational exercises:

1) Sixty percent of the 8000 students at the University of Southern North Dakota at Hoople (UofSNDatH) are female. One third of the women and one half of the men at the school are majoring in Business; the rest are in Arts & Sciences.

a) Give a contingency table for these data.

b) What is the probability that an Arts & Sciences student is male?

c) What is the probability that a male student is in Arts & Sciences?

d) Are major and gender independent or dependent? Explain.

2) SpamStopper is a commercial software product for filtering junk email. They claim to filter out 99% of incoming spam. (Unfortunately, they also filter out one out of every thousand "real" emails.)

a) Industry data indicate that forty percent of all email sent today is spam. (This percentage is growing rapidly, by the way.) If that’s the case, out of 10,000 total emails (both legitimate and otherwise), how many will SpamStopper filter out?

b) What percentage of filtered email should SpamStopper actually have delivered?

3) Medical researchers at the University of Southern North Dakota at Hoople recently announced discovery of a genetic condition linked to cancer. Specifically, persons who have a particular gene marker on the fourth chromosome have been shown to be predisposed to cancer of the ingrown toenail (CoIT, for short). Their research has shown that 2% of the population has this gene. Moreover, half of those with the gene eventually contract CoIT, while only 5% of those who do not have the gene will get CoIT.

a) Overall, what percentage of the population will get CoIT?

b) Balph Snerdwell has just been diagnosed with CoIT. What is the probability that he has the gene that is linked to the disease?

SOLUTIONS:
1b) 1/3     1c) 1/2     1d) dependent
2a) 3966     2b) .15%
3a) 5.9%     3b) .169