3.1 Homework (modified r. bloom)  (Page 3/6)

The following table identifies a group of children by one of four hair colors, and by type of hair.

• a Complete the table above.
• b What is the probability that a randomly selected child will have wavy hair?
• c What is the probability that a randomly selected child will have either brown or blond hair?
• d What is the probability that a randomly selected child will have wavy brown hair?
• e What is the probability that a randomly selected child will have red hair, given that he has straight hair?
• f If B is the event of a child having brown hair, find the probability of the complement of B.
• g In words, what does the complement of B represent?

A previous year, the weights of the members of the San Francisco 49ers and the Dallas Cowboys were published in the San Jose Mercury News . The factual data are compiled into the following table.

For the following, suppose that you randomly select one player from the 49ers or Cowboys.

• a Find the probability that his shirt number is from 1 to 33.
• b Find the probability that he weighs at most 210 pounds.
• c Find the probability that his shirt number is from 1 to 33 AND he weighs at most 210 pounds.
• d Find the probability that his shirt number is from 1 to 33 OR he weighs at most 210 pounds.
• e Find the probability that his shirt number is from 1 to 33 GIVEN that he weighs at most 210 pounds.
• f If having a shirt number from 1 to 33 and weighing at most 210 pounds were independent events, then what should be true about $\text{P(Shirt\# 1-33 | ≤ 210 pounds)}$ ?

Approximately 249,000,000 people live in the United States. Of these people, 31,800,000 speak a language other than English at home. Of those who speak another language at home, over 50 percent speak Spanish. ( Source: U.S. Bureau of the Census, 1990 Census )

Let: $E$ = speak English at home; $\mathrm{E\text{'}}$ = speak another language at home; $S$ = speak Spanish at home

Finish each probability statement by matching the correct answer.

The probability that a male develops some form of cancer in his lifetime is 0.4567 (Source: American Cancer Society). The probability that a male has at least one false positive test result (meaning the test comes back for cancer when the man does not have it) is 0.51 (Source: USA Today). Some of the questions below do not have enough information for you to answer them. Write “not enough information” for those answers.

Let: $C$ = a man develops cancer in his lifetime; $P$ = man has at least one false positive

• a Construct a tree diagram of the situation.
• b $\mathrm{P(C)}$ =
• c $P\mathrm{(P|C)}$ =
• d $P\mathrm{(P|C\text{'}\; )}$ =
• e If a test comes up positive, based upon numerical values, can you assume that man has cancer? Justify numerically and explain why or why not.

In 1994, the U.S. government held a lottery to issue 55,000 Green Cards (permits for non-citizens to work legally in the U.S.). Renate Deutsch, from Germany, was one of approximately 6.5 million people who entered this lottery. Let $\text{G = won Green Card}$ .

• a What was Renate’s chance of winning a Green Card? Write your answer as a probability statement.
• b In the summer of 1994, Renate received a letter stating she was one of 110,000 finalists chosen. Once the finalists were chosen, assuming that each finalist had an equal chance to win, what was Renate’s chance of winning a Green Card? Let $\text{F = was a finalist}$ . Write your answer as a conditional probability statement.
• c Are $G$ and $F$ independent or dependent events? Justify your answer numerically and also explain why.
• d Are $G$ and $F$ mutually exclusive events? Justify your answer numerically and also explain why.