Probability Problem Set

1. It takes five people working on different tasks to produce a new product. A small workplace has five
different workers and the plant manager wants to experimentally compare which workers/job
combinations produce the product in the fastest time. If they wanted to perform this experiment, how
many different combinations must they analyze?

2. Domino’s Pizza offers pizzas with two different sizes, three different types of crusts and up to 10
toppings. For topping you have a choice of having or not having.
How many different types of pizzas can be made?

3. To win the Texas Two-Step lotto game, players must match 4 lotto balls, drawn from 1-35 and a bonus
ball, drawn from another pool of numbers, also numbered 1-35. What is the probability that numbers
drawn at random will match the winning numbers?

4. An economics exam has 10 questions. The student must answer 3 of the first 4 and 2 of the last 6. How
many different sets of questions can a student elect to answer?

5. A 25 member sorority must choose its three officers: president, vice president and treasurer. How many
different slates of officers (president, vice president, treasurer) are possible in this sorority?

6. According to the 2000 Census 15.1% of Maryland residents live in Prince George’s (PG) county, 27.9%
of Maryland residents are African American, and 9.5% of Maryland are both PG County residents and
African American?.
A) What fraction of the population that is either a PG county resident or African American?
B) What fraction of the population that is either a PG county resident or non-African American?
C) What is the fraction of the population that is a non-PG county resident and African American?

7. A college senior has applied for admission to two medical schools, A and B. She estimates the
probability of acceptance at A at 0.7 and the probability of acceptance at B at 0.4 and the probability that
she will be admitted to both at 0.2. What is the chance she will not be accepted at either school?