   Chapter 8.4, Problem 5E ### Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203

#### Solutions

Chapter
Section ### Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203
Textbook Problem

# Recall from Example 1 that whenever Suzan sees a bag of marbles, she grabs a handful at random. In Exercises 1–10, she has seen a bag containing four red marbles, three green ones, two white ones, and one purple one. She grabs five of them. Find the probabilities of the following events, expressing each as a fraction in lowest terms. [HinT: See Example 1.]She has two red ones and one of each of the other colors.

To determine

To calculate: The probability that Suzan grabs two red marbles and one of each other colors, as a fraction in lowest terms, if the bag contains four red marbles, three green marbles, two white marbles and one purple marble and Suzan grabs five marbles.

Explanation

Given Information:

A bag contains four red marbles, three green marbles, two white marbles and one purple marble and Suzan grabs five marbles.

Formula used:

The probability of an event E, for sample space S is

P(E)=n(E)n(S)

According to the law of combination, the combination, C(n,r), is solved as,

C(n,r)=n!r!(nr)!

According to the rule for factorials, an n factorial is solved as,

n!=n(n1)...(3)(2)(1)

Calculation:

Consider the event that Suzan grabs two red marbles and one of each other colors to be E.

There are four red marbles, three green marbles, two white marbles and one purple marble in the bag.

Apply the formula for combination to find the total number ways to draw 5 marbles by substituting 10 for n and 5 for r,

n(S)=C(10,5)=10!5!(105)!=10!5!5!

Simplify using the property of factorials,

n(S)=1098765!(54321)5!=3242=252

Suzan grabs five marbles, there were 2 red balls, 1 green ball, 1 white ball and 1 purple ball.

Apply the formula for combination to find the total number ways to draw 2 red marbles by substituting 4 for n and 2 for r,

n(Red)=C(4,2)=4!2!(42)!=4!2!2!

Simplify using the property of factorials,

n(Red)=432!(21)2!=23=6

Apply the formula for combination to find the total number ways to draw 1 green marble by substituting 3 for n and 1 for r,

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