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Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742

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BuyFindarrow_forward

Algebra and Trigonometry (MindTap ...

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

SKILLS

17-20 Probability Distribution A binomial experiment with probability of success p is performed n times. (a) Make a table of the probability distribution. (b) Draw a probability histogram.

n = 5 , p = 0.4

To determine

(a)

To make:

The table of probability distribution.

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 number of independent trial is,

n=5

The probability of success is,

p=0.4

Calculate the probability of 0 success.

Substitute 0 for r, 0.4 for p and 5 for n in equation (1).

P(0)=5!0!(50)!(0.4)0(10.4)50=1(1)(0.07776)=0.07776=2433125

Calculate the probability of 1 success.

Substitute 1 for r, 0.4 for p and 5 for n in equation (1).

P(1)=5!1!(51)!(0.4)1(10.4)51=5(0.4)(0.1296)=0.2592=162625

Calculate the probability of 2 success.

Substitute 2 for r, 0.4 for p and 5 for n in equation (1).

P(2)=5!2!(52)!(0.4)2(10.4)52=10(0.16)(0.216)=0

To determine

(b)

To draw:

The probability histogram.

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Chapter 14 Solutions

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