2
AssignmentMultiple Select

Probability with Combinations and Permutations

Question 2 • Fall 24 GMS Geometry: Concepts and Connections B

There are 10 boys and 12 girls in the tennis club. The coach wants to select two players to practice first. Which statements are true? Check all that apply.There is approximately a 27 percent likelihood that one boy and one girl will be chosen to practice first.There is approximately a 52 percent likelihood that one boy and one girl will be chosen to practice first.There is approximately a 19 percent likelihood that two boys will be chosen to practice first.There is approximately a 19 percent likelihood that two girls will be chosen to practice first.There is approximately a 29 percent likelihood that two girls will be chosen to practice first.

Answer
A
There is approximately a 27 percent likelihood that one boy and one girl will be chosen to practice first.
B
There is approximately a 52 percent likelihood that one boy and one girl will be chosen to practice first.
C
There is approximately a 19 percent likelihood that two boys will be chosen to practice first.
D
There is approximately a 19 percent likelihood that two girls will be chosen to practice first.
E
There is approximately a 29 percent likelihood that two girls will be chosen to practice first.

Explanation

There are 22 players, so there are 22 × 21 ÷ 2 = 231 possible pairs. One boy and one girl can be chosen in 10 × 12 = 120 ways, giving about 120 ÷ 231 ≈ 52%. Two boys can be chosen in 10 × 9 ÷ 2 = 45 ways, or about 19%; two girls can be chosen in 12 × 11 ÷ 2 = 66 ways, or about 29%.

AI-written and checked against the verified answer.

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