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Chapter 2: Q. 2.31 (page 50)

A 3-personal basketball team consists of a guard, a forward, and a center.

(a)If a person is chosen at random from each of three different such teams, what is the probability of selecting a complete team?

(b)What is the probability that all 3players selected play the same position?

Short Answer

Expert verified

a)29b)19

Step by step solution

01

Given Information.

A 3personal basketball team consists of a guard, a forward, and a center.

02

Part (a) Explanation.

We have3choices for a guard from the3teams.2choices for a forward once we have chosen the guard and no choice for a center once we have chosen a guard and a forward. This gives us 3脳2=6possible teams which have each member from a different team. Total possible teams will simply be27as each member can be chosen from 3different teams having 3players each33.

03

Part (b) Explanation.

The probability of the team being all 3guards is13脳13脳13=127.

Same probability for the team being all forwards and all centers. This is calculated by using the fact that choosing a guard/forward/center from a team has a probability13.

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