Counting, Permutations, Combinations and Probability: Precalculus Math Test – PDF Download

Question 1: Counting routes (2 points)

A road map shows 3 roads from Home to the Mall and 4 roads from the Mall to the Beach.

1. How many one-way routes lead from Home to the Beach through the Mall? (1 point)
2. How many round trips are possible if any road may be used in either direction? (1 point)

Question 2: Permutations and combinations (2 points)

Evaluate each expression.

1. \(_{9}P_{3}\) (1 point)
2. \(_{9}C_{3}\) (1 point)

Question 3: Arranging letters (2 points)

Find the number of distinct arrangements of all the letters in BOOKKEEPER.

Question 4: Forming a team (3 points)

A club has 7 boys and 5 girls. A team of 4 is chosen.

1. How many teams are possible? (1 point)
2. How many teams have exactly 2 girls? (1 point)
3. If the team is chosen at random, what is the probability that it has exactly 2 girls? (1 point)

Question 5: Three spades (2 points)

Three cards are dealt from a standard 52-card deck. Find the probability that all three are spades.

Question 6: Two draws (3 points)

A bag holds 6 white and 4 black marbles. Two marbles are drawn without replacement, as shown in the incomplete tree.

1. Find the probability that both marbles are white. (1 point)
2. Find the probability that the marbles are different colors. (2 points)

Question 7: Expected value (3 points)

The bar graph shows the probability distribution of a random variable \(X\). The probability for \(x=4\) is missing.

1. Find \(P(X=4)\). (1 point)
2. Find \(E(X)\). (2 points)

Question 8: Carnival game (3 points)

Liam pays $4 to draw one card from 20 cards. One card pays $30, four cards pay $5 each, and the other cards pay nothing. Find the expected net result per play and interpret it.

⬇ Download the Precalculus Counting, Permutations, Combinations and Probability test (PDF, 79 KB)

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