Use the following information to answer the next seven exercises: An article in the New England Journal of Medicine, reported about a study of people who use a product in California and Hawaii. In one part of the report, the self-reported ethnicity and using the product levels per day were given. Of the people using the product at most 10 times a day, there were 9,886 African Americans, 2,745 Native Hawaiians, 12,831 Latinos, 8,378 Japanese Americans, and 7,650 whites. Of the people using the product 11 to 20 times per day, there were 6,514 African Americans, 3,062 Native Hawaiians, 4,932 Latinos, 10,680 Japanese Americans, and 9,877 whites. Of the people using the product 21 to 30 times per day, there were 1,671 African Americans, 1,419 Native Hawaiians, 1,406 Latinos, 4,715 Japanese Americans, and 6,062 whites. Of the people using the product at least 31 times per day, there were 759 African Americans, 788 Native Hawaiians, 800 Latinos, 2,305 Japanese Americans, and 3,970 whites.

Complete the table using the data provided. Suppose that one person from the study is randomly selected. Find the probability that person used the product 11 to 20 times a day.

Product Use (times per day) | African Americans | Native Hawaiians | Latinos | Japanese Americans | Whites | TOTALS |
---|---|---|---|---|---|---|

1–10 | ||||||

11–20 | ||||||

21–30 | ||||||

31+ | ||||||

TOTALS |

Suppose that one person from the study is randomly selected. Find the probability that the person used the product 11 to 20 times per day.

Find the probability that the person was Latino.

In words, explain what it means to pick one person from the study who is Japanese American **AND** uses the product 21 to 30 times per day. Also, find the probability.

In words, explain what it means to pick one person from the study who is Japanese American **OR** uses the product 21 to 30 times per day. Also, find the probability.

In words, explain what it means to pick one person from the study who is Japanese American **GIVEN** that the person uses the product 21 to 30 times per day. Also, find the probability.

Prove that product use/day and ethnicity are dependent events.