Q. 2.32 A group of individuals containin... [FREE SOLUTION]

91影视

A First Course in Probability

Sheldon M. Ross

$Math Studyset 91影视 Explanations$ Math

9th Edition 路 432 pages

ISBN: 9780321794772

Chapter 2: Q. 2.32 (page 50)

A group of individuals containing $b$ boys and $g$ girls is lined up in random order; that is, each of the $(b + g)!$ permutations is assumed to be equally likely. What is the probability that the person in the ith position, role="math" localid="1648906629368" $1 鈮� i 鈮� b + g,$ is a girl?

Short Answer

Expert verified

The probability that the person in the ith position, $1 鈮� i 鈮� b + g,$ a girl is $\frac{g}{b + g}$ .

Step by step solution

Given Information.

A group of individuals containing $b$ boys and $g$ girls is lined up in random order; that is, each of the $(b + g)!$ permutations is assumed to be equally likely.

Explanation.

$\frac{(\begin{array}{l} g \\ 1 \end{array}) (b + g - 1)!}{(b + g)!} = \frac{g}{b + g}$

We choose one girl from the $g$ availablelocalid="1648907482431" $(\begin{array}{l} g \\ 1 \end{array})$ ways. We arrange the remaining localid="1648907491200" $(b + g - 1)$ people in the $(b + g - 1)$ positions. Ipar We divide this by the total arrangements $(b + g)!$ .

Explanation.

the probability that the person in the ith position, $1 鈮� i 鈮� b + g,$ a girl is $\frac{g}{b + g}$ .

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91影视

A group of individuals containing $b$ boys and $g$ girls is lined up in random order; that is, each of the $(b + g)!$ permutations is assumed to be equally likely. What is the probability that the person in the ith position, role="math" localid="1648906629368" $1 鈮� i 鈮� b + g,$ is a girl?

Short Answer

Step by step solution

Given Information.

Explanation.

Explanation.

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91影视

A group of individuals containing bboys and ggirls is lined up in random order; that is, each of the(b+g)!permutations is assumed to be equally likely. What is the probability that the person in the ith position, role="math" localid="1648906629368" 1鈮�i鈮�b+g, is a girl?

Short Answer

Step by step solution

Given Information.

Explanation.

Explanation.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Decision Maths

Discrete Mathematics

Calculus

Probability and Statistics

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

A group of individuals containing $b$ boys and $g$ girls is lined up in random order; that is, each of the $(b + g)!$ permutations is assumed to be equally likely. What is the probability that the person in the ith position, role="math" localid="1648906629368" $1 鈮� i 鈮� b + g,$ is a girl?