8
QuizMultiple Choice

Probability — Test

Question 8 • Algebra 2 with Probability

Five students want to play dodgeball and they all want to be a team captain. To be fair, the gym coach decides to place the names of all five students into a hat, mix well, and select two names at random without replacement. The names chosen will be the team captains. Each outcome in the sample space for the random selection of two team captains is equally likely. What is the probability of each outcome in the sample space?

Answer
A
1 tenth
B
1 over 20
C
1 fifth
D
1 over 25

Explanation

Because two names are selected from five without replacement, the outcomes are pairs of students. There are 5 × 4 = 20 ways to select two names in order, but each pair can be drawn in either order, so there are 20 ÷ 2 = 10 equally likely outcomes. Each outcome therefore has probability 1/10, which is choice A, “1 tenth.”

AI-written and checked against the verified answer.

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