There are 3 boys and 2 girls at a party. Three party-goers are selected at random to go on a root-beer run. Let W denote the number of girls in the group of three that go on the root-beer run. Compute the expected number of girls who go on the root-beer run, E[W].

There are 3 boys and 2 girls at a party. Three party-goers are selected at random to go on a root-beer run. Let W denote the number of girls in the group of three that go on the root-beer run. Compute the expected number of girls who go on the root-beer run, E[W].

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Question

There are 3 boys and 2 girls at a party.
Three party-goers are selected at random to
go on a root-beer run. Let W denote the
number of girls in the group of three that go
on the root-beer run.
Compute the expected number of girls who
go on the root-beer run, E[W].

Expert Solution

Step 1

There are 3 boys and 2 girls at the party.

Three party-goers are selected at random to go on the root beer run.

An event $W$ is a number of girls in a group of three that go on the root beer run.

The expected value formula is as follows

$E [W] = \sum_{i = 1}^{n} w_{i} P (W = w_{i})$

The combination formula is as follows.

${}^{n}{C_{x} = \frac{n!}{(n - x)! x!}}$

The factorial is as follows.

$n! = n \times (n - 1) \times (n - 2) \times . . . \times 1$

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