Counting Probability Test – Precalculus Math (Printable PDF)

Question 1 Full Meals (2 points)

A restaurant offers 4 appetizers, 6 entrees and 3 desserts. A full meal has one of each.

1. How many different full meals are possible? (1 point)
2. How many meal choices are possible if the dessert is optional (a diner may skip it)? (1 point)

Question 2 Permutation or Combination (2 points)

Evaluate P(7, 3) and C(7, 3). Then explain in one sentence why they are different.

Question 3 Random Committee (3 points)

A committee of 3 is chosen at random from 6 boys and 4 girls.

1. How many different committees are possible? (1 point)
2. Find the probability that exactly 2 members are girls. (1 point)
3. Find the probability that at least one member is a girl. (1 point)

Question 4 Trophy Shelf (2 points)

Five different trophies are placed in a row. (a) How many arrangements are there? (b) How many have the tallest trophy in the middle position?

Question 5 Marbles Without Replacement (3 points)

A bag holds 5 red and 3 white marbles. Two are drawn without replacement.

1. Find the four second-draw probabilities marked ? in the tree. (1 point)
2. Find the probability that both marbles are red. (1 point)
3. Find the probability that the marbles are different colors. (1 point)

Question 6 Expected Value of a Game (3 points)

X is a player’s net gain in dollars in a game. The chart shows its distribution.

1. Show that the probabilities form a valid distribution. (1 point)
2. Find E(X). (1 point)
3. Explain what E(X) means for a player. (1 point)

Question 7 Die Game (3 points)

A player pays $5 to roll a fair die. Rolling a 6 wins $12, rolling a 4 or a 5 wins $3, and any other roll wins nothing. Should the player expect to come out ahead? Show the distribution of the winnings, the expected winnings and the expected net gain.

Question 8 Pets Survey (2 points)

Forty students were asked how many pets they have. The counts were 0 pets: 8 students, 1 pet: 16, 2 pets: 10, 3 pets: 6. Write the empirical probability distribution and find the expected number of pets.