91Ó°ÊÓ

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.

a. Construct a table or a tree diagram of the situation. Include a branch for all other modes of transportation to work.

b. Assuming that the walkers walk alone, what percent of all commuters travel alone to work?

c. Suppose that$1,000$ workers are randomly selected. How many would you expect to travel alone to work?

d. Suppose that $1,000$ workers are randomly selected. How many would you expect to drive in a carpool?

When the Euro coin was introduced in $2002$, two math professors had their statistics students test whether the Belgian one Euro coin was a fair coin. They spun the coin rather than tossing it and found that out of $250$spins,$140$showed a head (event H) while $110$showed a tail (event T). On that basis, they claimed that it is not a fair coin.

a. Based on the given data, find P(H) and P(T).

b. Use a tree to find the probabilities of each possible outcome for the experiment of tossing the coin twice.

c. Use the tree to find the probability of obtaining exactly one head in two tosses of the coin.

d. Use the tree to find the probability of obtaining at least one head

Use the following information to answer the next two exercises. The following are real data from Santa Clara County, CA. As of a certain time, there had been a total of $3,059$documented cases of AIDS in the county. They were grouped into the following categories:

Suppose a person with AIDS in Santa Clara County is randomly selected.

a. Find P(Person is female).

b. Find P(Person has a risk factor heterosexual contact).

c. Find P(Person is female OR has a risk factor of IV drug user).

d. Find P(Person is female AND has a risk factor of homosexual/bisexual).

e. Find P(Person is male AND has a risk factor of IV drug user).

f. Find P(Person is female GIVEN person got the disease from heterosexual contact).

g. Construct a Venn diagram. Make one group females and the other group heterosexual contact

Answer these questions using probability rules. Do NOT use the contingency table. Three thousand fifty-nine cases of AIDS had been reported in Santa Clara County, CA, through a certain date. 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.

a. Find P(Person is female).

b. Find P(Person obtained the disease through heterosexual contact).

c. Find P(Person is female GIVEN person got the disease from heterosexual contact)

d. Construct a Venn diagram representing this situation. Make one group females and the other group heterosexual contact. Fill in all values as probabilities.

Use the following information to answer the next six exercises. There are 23 countries in North America, 12 countries in

South America, 47 countries in Europe, 44 countries in Asia, 54 countries in Africa, and 14 in Oceania (Pacific Ocean

region).

Let A = the event that a country is in Asia.

Let E = the event that a country is in Europe.

Let F = the event that a country is in Africa.

Let N = the event that a country is in North America.

Let O = the event that a country is in Oceania.

Let S = the event that a country is in South America.

Find P(E).

Use the following information to answer the next six exercises. There are 23 countries in North America, 12 countries in South America, 47 countries in Europe, 44 countries in Asia, 54 countries in Africa, and 14 in Oceania (Pacific Ocean

region).

Let A = the event that a country is in Asia.

Let E = the event that a country is in Europe.

Let F = the event that a country is in Africa.

Let N = the event that a country is in North America.

Let O = the event that a country is in Oceania.

Let S = the event that a country is in South America.

Find P(N).

What is the probability of drawing a club in a standard deck of $52$cards?

Use the following information to answer the next four exercises. A box Is filled with several party favours. It contains 12 hats, 15 noisemakers, ten finger traps, and five bags of confetti.

Let H : the event of getting a hat.

Let N= the event of getting a noisemaker.

Let F= the event of getting a finger trap.

Let C= the event of getting a bag of confetti.

Find P(H)

What is the probability of rolling an even number of dots with a fair, six-sided die numbered one through six?

What is the probability of rolling a prime number of dots with a fair, six-sided die numbered one through six?