1. You draw one card from a deck of 52. If you get a heart, you win $18. If you get anything else, you pay $5. Note that there are 13 hearts in the deck. What is the expected value of the game?
2. A class has sophomores and juniors, and biology and history majors. The table below shows the number of students in each category. (There are no double-majors.)
|
Biology
|
History
|
|
Sophomores
|
15
|
13
|
|
Juniors
|
12
|
10
|
a) If one student is chosen at random, what is the probability of selecting a biology major?
b) If one student is chosen at random, what is the probability of selecting a biology major or a sophomore?
c) If two students are chosen at random, what is the probability of selecting a junior history major and then another junior history major? The selections are made without replacement.
d) If one student is chosen at random, what is the probability of selecting a junior, given that the student chosen is a biology major?
3. A club has 14 members. Five will be chosen to attend a conference. In how many ways can this be done?
4. A club has 12 members. A president and a vice-president must be chosen. In how many ways can this be done?
5. A team has an 85% chance of winning each game that it plays. What is the probability that the team will win exactly 5 of its next 7 games? Use the binomial distribution for this problem.
6. A bank knows that only 5% of its loans ever default. Out of a group of 8 loans, what is the probability that at least one loan will default? Use the binomial distribution for this problem.
7. Student scores on an exam have an average of 72.4 with a standard deviation of 9.8. The scores are normally distributed.
a) If one student is selected at random, what is the probability that the student scored greater than 81?
b) If one student is selected at random, what is the probability that the student scored less than 92?
c) If one student is selected at random, what is the probability that the student scored between 60 and 74?
d) What score is the 75th percentile?