There are four major blood types in humans: O, A, B, and AB. In a study conducted using blood specimens from the Blood Bank of Hawaii, individuals were classified according to blood type and ethnic group. The ethnic groups were Hawaiian, Hawaiian-White, Hawaiian-Chinese, and White.

Suppose that a blood bank specimen is selected at random.

Ethnic Group Blood type Hawaiians Hawaiian-

White Hawaiian-

Chinese White Total O 1903 4469 2206 53,759 62,337 A 2490 4671 2368 50,008 59,537 B 178 606 568 16,252 17,604 AB 99 236 243 5001 5579 Total 4670 9982 5385 125,020 145,057

(a) Find the probability that the specimen contains type O blood or comes from the Hawaiian-Chinese ethnic group. Show your work.

(b) What is the probability that the specimen contains type AB blood, given that it comes from the Hawaiian ethnic group? Show your work.

(c) Are the events “type B blood” and “Hawaiian ethnic group” independent? Give appropriate statistical evidence to support your answer.

(d) Now suppose that two blood bank specimens are selected at random. Find the probability that at least one of the specimens contains type A blood from the White ethnic group.