Algebra II Hon: Probability 2 Worksheet
1. A committee of four students is to be formed from members of the student council. The student council
contains 13 girls and 12 boys.
a. How many different committees of four students are possible?
b. How many committees will contain only boys?
c. What is the probability that the committee will contain only boys?
2. A jar of marbles contains six yellow and eight red marbles. Three marbles are selected at random.
a. How many different groups of three marbles are possible?
b. How many groups of three marbles will contain only red ones?
c. What is the probability that the group of marbles will contain only red marbles?
3. The letters of the alphabet are written on slips of paper and placed in a hat. Three letters are selected at
random.
a. How many different combinations of three letters are possible?
b. How many combinations consist only of the letters A, C, H, I, K, or Y?
c. What is the probability that the letters selected consist only of the letters A, C, H, I, K, or Y?
4. Three cards are selected at random from a standard deck of 52 playing cards. What is the probability that all
three are Face cards (Jack, Queen, or King)?
5. A lottery requires that you match three numbers in order. The three numbers are chosen from the numbers
1-20. What is the probability that you will win this lottery if each number can be chosen only once?
6. A basketball player shoots about 42% from the three-point line. What is the probability that she will make
exactly 2 out of her next 5 shots?
7.
A basketball player shoots about 56% from the free-throw line. What is the probability that she will make
exactly 6 out of her next 8 free-throws?
8. A family has 7 children. Assume that the probability of having a boy is 50%. What is the probability that
they will have exactly 3 boys?
9. For a group of 40 people, what is the probability that exactly 3 people in the group will celebrate their
birthdays on a Wednesday this year?
10. You roll a number cube 4 times. What is the probability that you will roll a number greater than 4 on
exactly 3 of the rolls?
11. The probability that a driver is not wearing his seatbelt is 0.18%. Find the probability that at least 3 out of
5 drivers are not wearing seatbelts?
12. In 1997, 40% of U.S. households owned at least one cell phone. What is the probability that at least 10 out
of 13 U.S. households owned a cell phone?
13. A medical center has 12 ambulances. Given an ambulance’s current condition, regular maintenance, and
restocking of medical supplies, the probability of an ambulance being operational is 93%. Find the
probability that at least 2 of the ambulances are operational at a given time.
14. A survey of 4826 randomly selected young adults (aged 19 to 25) asked, “What do you think are the
chances you will have much more than a middle-class income at age 30?” Choose a survey respondent at
random.
Gender
Opinion
Almost no chance
Female
96
Male
98
Total
194
Some chance but probably not
426
286
712
A 50-50 chance
696
720
1416
A good chance
663
758
1421
Almost certain
486
597
1083
Total
2367
2459
4826
a. Given that the person selected is male, what’s the probability that he answered “Almost certain”?
b. If the person selected said “Some chance but probably not,” what’s the probability that the person is
female?
c. Find P(“a good chance” | female).
15. In 1912 the luxury liner Titanic, on its first voyage across the Atlantic, struck an iceberg and sank. Some
passengers got off the ship in lifeboats, but many died. Suppose we choose and adult passenger at random.
Class of Travel
First class
Survival Status
Lived
Died
197
122
Second class
94
167
Third class
151
476
a. Given that the person selected was in first class, what’s the probability that he or she survived?
b. If the person selected survived, what’s the probability that he or she was a third-class passenger?
c. Find P(survived | second class).