Summary: This module provides a number of homework exercises related to Probability.
Suppose that you have 8 cards. 5 are green and 3 are yellow. The 5 green cards are numbered 1, 2, 3, 4, and 5. The 3 yellow cards are numbered 1, 2, and 3. The cards are well shuffled. You randomly draw one card.
Refer to the previous problem. Suppose that this time you randomly draw two cards, one at a time, and with replacement.
Refer to the previous problems. Suppose that this time you randomly draw two cards, one at a time, and without replacement.
Roll two fair dice. Each die has 6 faces.
A special deck of cards has 10 cards. Four are green, three are blue, and three are red. When a card is picked, the color of it is recorded. An experiment consists of first picking a card and then tossing a coin.
An experiment consists of first rolling a die and then tossing a coin:
An experiment consists of tossing a nickel, a dime and a quarter. Of interest is the side the coin lands on.
Consider the following scenario:
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The following are real data from Santa Clara County, CA. As of March 31, 2000, there was a total of 3059 documented cases of AIDS in the county. They were grouped into the following categories (Source: Santa Clara County Public H.D.):
| Homosexual/Bisexual | IV Drug User* | Heterosexual Contact | Other | Totals | |
|---|---|---|---|---|---|
| Female | 0 | 70 | 136 | 49 | ____ |
| Male | 2146 | 463 | 60 | 135 | ____ |
| Totals | ____ | ____ | ____ | ____ | ____ |
Suppose one of the persons with AIDS in Santa Clara County is randomly selected. Compute the following:
The completed contingency table is as follows:
| Homosexual/Bisexual | IV Drug User* | Heterosexual Contact | Other | Totals | |
|---|---|---|---|---|---|
| Female | 0 | 70 | 136 | 49 | 255 |
| Male | 2146 | 463 | 60 | 135 | 2804 |
| Totals | 2146 | 533 | 196 | 174 | 3059 |
Solve these questions using probability rules. Do NOT use the contingency table above. 3059 cases of AIDS had been reported in Santa Clara County, CA, through March 31, 2000. Those cases will be our population. Of those cases, 6.4% obtained the disease through heterosexual contact and 7.4% are female. Out of the females with the disease, 53.3% got the disease from heterosexual contact.
The following table identifies a group of children by one of four hair colors, and by type of hair.
| Hair Type | Brown | Blond | Black | Red | Totals |
|---|---|---|---|---|---|
| Wavy | 20 | 15 | 3 | 43 | |
| Straight | 80 | 15 | 12 | ||
| Totals | 20 | 215 |
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