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Probability and Events of Disease Control

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1. The following table, based on the data from the Centers for Disease Control, gives the number of new cases of the AIDS virus for men and women in the United States in 1998 by method of transmission.

Method of Transmission Male Female Total

Homosexual contact 8388 0 8388
Heterosexual contact 1146 1806 2952
Intravenous drug use 3652 1541 5193
Other 5237 2054 7291
Total 18423 5401 23824

a. Find the probability that a male resident who was newly diagnosed with AIDS in 1998 contracted it via homosexual contact.
b. Find the probability that a female resident who was newly diagnosed with AIDS in 1998 contracted it via intravenous drug use.

2. A company sells printers and copiers. Let E be the event "a customer buys a printer," and let F be the event "a customer buys a copier." Write the following use Intersection (upsidedown U), Union(U), or ' as necessary.

a. A customer buys neither machine.

b. A customer buys at least one of the machines.

3. The probability that a certain machine turns out a defective item is .05. Find the probabilities that in a run of 75 items, the following results are obtained.

a. Exactly 5 defective items

b. No defective items

c. At least 1 defective item

4. In a club with 20 senior and 10 junior members, what is the expected number of junior members on a 3-member committee?

keywords: probabilities

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Probability
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1. The following table, based on the data from the Centers for Disease Control, gives the number of new cases of the AIDS virus for men and women in the United States in 1998 by method of transmission.

Method of Transmission Male Female Total

Homosexual contact 8388 0 8388
Heterosexual contact 1146 1806 2952
Intravenous drug use 3652 1541 5193
Other 5237 2054 7291
Total 18423 ...

Solution provided by:
Changping Wang, MA
Education
  • BSc , Wuhan Univ. China
  • MA, Shandong Univ.
Recent Feedback
  • "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
  • "excellent work"
  • "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
  • "Thank you"
  • "Thank you very much for your valuable time and assistance!"
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