   Chapter 14.3, Problem 14E ### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742

#### Solutions

Chapter
Section ### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742
Textbook Problem

# SKILLS3-14 Binomial Trials Five independent trials of a binomial experiment with probability of success p = 0.7 are performed. Find the probability of each event.At most three failure.

To determine

To find:

The probability of at most three failure.

Explanation

Approach:

The probability of getting exactly r successes in n independent trials of the experiment is

P(rsuccessesinntrials)=C(n,r)pr(1p)nr=n!r!(nr)!pr(1p)nr ...... (1)

The probability of failure is given as:

P(failure)=1p ……(2)

Calculation:

The probability of success is,

p=0.7

The number of trials is,

n=5

The probability of failure,

1p=(10.7)=0.3

Calculate the probability of at most two failure.

P(atmost3failure)=P(atleast2successes)=(P(2successes)+P(3successes)+P(4successes)+P(5successes)) ……(3)

Calculate the probability of exactly 2 successes.

Substitute the values 5 for n, 0.7 for p and 2 for r in equation (1).

P(2successes)=5!2!(53)2!0.72(10.7)52=10(0.49)(0.027)=0.1323

Calculate the probability of exactly 3 successes.

Substitute the values 5 for n, 0.7 for p and 3 for r in equation (1)

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