## Stochastic Processes and Trees - High School Math

Assume that 60 percent of the students at the university have taken 4 years of high school math. Of those with four years of high school math, 65 percent plan to major in science. Of those without 4 years, only 10 percent plan to major in science. You stop a student at random. If the student plans to major in science, what is the probability that this student had four years of high school math?

## Stochastic Processes and Trees - Vehicles in a Fleet

Assume that the fleet consists of 30 percent Lexus, 20 percent Infinity, and 50 percent Mercedes automobiles. 75 percent of the Lexus cars, 70 percent of the Infinities, and 55 percent of the Mercedes have CD players.

Use this information to answer the following questions.

What is the probability that a randomly selected car has a CD player?

What is the probability that a randomly selected car either is a Mercedes or has a CD player?

## Stochastic Processes and Trees - Number of Science Majors

Assume that 20 percent of students have taken calculus in high school. Of those who have taken calculus in high school, 70 percent plan to major in science. Of those who did not take calculus in high school, only 30 percent plan to major in science. What is the probability that a randomly selected student plans to major in science?

## Stochastic Processes and Trees - Three Men Coin Toss

Three men toss a fair coin to see who pays for lunch. If all three match, they toss again. Otherwise, the "odd man" pays for lunch. What is the probability that they will need to do this more than once? and what is the probability of tossing at most twice?

## Stochastic Processes and Trees - People in a Hotel

Mark, Nicole, Patrick, Rita, Sarah, Ulrich, and Vera are going to attend a conference at a Hilton Hotel. Each one will have a single room by herself or himself. When they arrive at the hotel (they drove together in a company van), there are 6 single rooms available on the sixth floor and 5 single rooms available on the seventh floor. Each person is assigned to one of these rooms.

In how many overall outcomes is Vera on the sixth floor (i.e., Vera's room is on the sixth floor)?

In how many overall outcomes are Patrick and Rita on the same floor?

In how many overall outcomes is Mark on a higher floor than Sarah?