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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

Pharmaceuticals A drug that is used to prevent motion sickness is found to be effective about 75 % of the time. Six friends, all prone to seasickness, go on a sailing cruise, and all take the drug. Find the probability of each event.

(a) None of the friends gets seasick.

(b) All of the friends get seasick.

(c) Exactly three get seasick.

(d) At least two get seasick.

To determine

(a)

To find:

The probability that none of the friends gets seasick.

Explanation

Given:

There are 6 friends.

The probability of drug being effective is 75%.

Approach:

Write the expression for the probability of success in a trial.

P(S)=p

Here, P(S) is the probability of success.

Write the expression to find the probability of failure in a trial.

P(F)=1pq=1p ……(1)

Here, q=P(F) is probability of failure.

Write the expression to find the probability of getting exactly r success in given number of independent trials of the experiment.

P(rsuccessesinntrials)=C(n,r)prqnr …... (2)

Here, n is the number of trial and r is the number of success in the given experiment.

Write the formula to find the number of combinations.

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

Substitute n!r!(nr)! for C(n,r) in equation (2). Then,

P(rsuccessesinntrials)=(n!r!(nr)!)prqnr ……(3)

To determine

(b)

To find:

The probability that all of the friends gets seasick.

To determine

(c)

To find:

The probability that exactly three gets seasick.

To determine

(d)

To find:

The probability that at least two get seasick.

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Chapter 14 Solutions

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