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:

EE size 12{E} {} and FF size 12{F} {} mutually exclusive events. P(E)=0.4P(E)=0.4 size 12{P \( E \) =0 "." 4} {}; P(F)=0.5P(F)=0.5 size 12{P \( F \) =0 "." 5} {}. Find P(E∣F)P(E∣F) size 12{P \( E \lline F \) } {}.

JJ size 12{J} {} and KK size 12{K} {} are independent events. P(J | K) = 0.3 P(J | K) = 0.3. Find P(J)P(J) size 12{P \( J \) } {} .

UU size 12{U} {} and VV size 12{V} {} are mutually exclusive events. P(U)=0.26P(U)=0.26 size 12{P \( U \) =0 "." "26"} {}; P(V)=0.37P(V)=0.37 size 12{P \( V \) =0 "." "37"} {}. Find:

QQ size 12{Q} {} and RR size 12{R} {} are independent events. P(Q) = 0.4P(Q) = 0.4 ; P(Q AND R) = 0.1P(Q AND R) = 0.1 . Find P(R)P(R).

YY size 12{Y} {} and ZZ size 12{Z} {} are independent events.

GG size 12{G} {} and HH size 12{H} {} are mutually exclusive events. P(G)=0.5P(G)=0.5 size 12{P \( G \) =0 "." 5} {}; P(H)=0.3P(H)=0.3 size 12{P \( H \) =0 "." 3} {}

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.):

Suppose one of the persons with AIDS in Santa Clara County is randomly selected. Compute the following:

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.

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.

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: EE = speak English at home; E'E' = speak another language at home; SS = 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: CC = a man develops cancer in his lifetime; P P = man has at least one false positive

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 G = won Green CardG = won Green Card.

Three professors at George Washington University did an experiment to determine if economists are more selfish than other people. They dropped 64 stamped, addressed envelopes with $10 cash in different classrooms on the George Washington campus. 44% were returned overall. From the economics classes 56% of the envelopes were returned. From the business, psychology, and history classes 31% were returned. (Source: Wall Street Journal)

Let: RR = money returned; EE = economics classes; OO = other classes

The chart below gives the number of suicides estimated in the U.S. for a recent year by age, race (black and white), and sex. We are interested in possible relationships between age, race, and sex. We will let suicide victims be our population. (Source: The National Center for Health Statistics, U.S. Dept. of Health and Human Services)

Complete the following:

Suppose that 10,000 U.S. licensed drivers are randomly selected.

Approximately 86.5% of Americans commute to work by car, truck or van. Out of that group, 84.6% drive alone and 15.4% drive in a carpool. Approximately 3.9% walk to work and approximately 5.3% take public transportation. (Source: Bureau of the Census, U.S. Dept. of Commerce. Disregard rounding approximations.)

Explain what is wrong with the following statements. Use complete sentences.