Abby, Deborah, Julie, Sam, and Roberto work in a firm's public relations office. Their employer must choose two of them to attend a conference in Paris. To avoid unfairness, the choice will be made by drawing two names from a hat. (This is an SRS of size 2.) Write down all possible choices of two of the five names. This is the sample space.

Choose a point at random in the graph of the square with sides

$$0 \leq x \leq 1$$

and

$$0 \leq y \leq 1$$

. Since the area of the squares is 1 unit, the probability that the point falls in any region within the square is the area of that region. Let X be the x coordinate and Y the y coordinate of the point chosen. Find the conditional probability P(Y < 1/2 | Y > X).

An examination consists of multiple-choice questions, each having five possible answers. Linda estimates that she has a probability of 0.75 of knowing the answer to any question that may be asked. If she does not know the answer, she will guess, with a conditional probability of 1/5 of being accurate. Determine the conditional probability that Linda knows the answer, given that she supplies the accurate answer.

Draw a tree diagram with probabilities for the race (white, black, or Hispanic) and vote (for or against the candidate of a randomly chosen voter. What percent of the overall vote does the candidate expect to get?

An examination consists of multiple choice questions, each having five possible answers. Linda estimates that she has probability 0.75 of knowing the answer to any question that may be asked. If she does not know the answer, she will guess, with conditional probability 1/5 of being correct. What is the probability that Linda gives the correct answer to a question? (Draw a tree diagram to guide the calculation.)

Suppose that the treasurer also feels that, if the dollar does not fall, there is probability 0.2 that the Japanese supplier will demand the contract be renegotiated. What is the probability that the supplier will demand renegotiation?

Use your work from the mentioned exercise to find the percent of A students who are involved in accidents.

What is the probability that a randomly chosen young driver is an A student and is involved in an accident?

Let A be the event that a young driver is an A student and C the event that a young driver is involved in an accident this year. State the information given in terms of probabilities and conditional probabilities for the events A and C.

Toss a thumbtack on a hard surface 100 times. How many times did it land with the point up? What is the approximate probability of landing point up?

When we toss a penny, experience shows that the probability (long-term proportion) of a head is close to 1/2. Suppose now that we toss the penny repeatedly until we get a head. What is the probability that the first head comes up in an odd number of tosses(1, 3, 5, and so on)? To find out, repeat this procedure 50 times, and keep a record of the number of tosses needed to get a head on each of your 50 trials. Use your results to estimate the probability that the first head appears on an odd numbered toss.

From your experiment, estimate the probability of a head on the first loss. What value should we expect this probability to have?

Here are the counts (in thousands) of earned degrees in the United States in a recent year, classified by level and by the sex of the degree recipient:

Use the multiplication rule to find the joint probability of choosing a male bachelor's degree recipient. Check your result by finding this probability directly from the table of counts.

Here are the counts (in thousands) of earned degrees in the United States in a recent year, classified by level and by the sex of the degree recipient:

What is the conditional probability that the person chosen received a bachelor's degree, given that he is a man?