Finite Mathematics

7th Edition
Stefan Waner + 1 other
ISBN: 9781337280426

Chapter
Section

Finite Mathematics

7th Edition
Stefan Waner + 1 other
ISBN: 9781337280426
Textbook Problem

Quality Control A manufacturer of light bulbs chooses bulbs at random from its assembly line for testing. If the probability of a bulb’s being bad is .01, how many bulbs does the manufacturer need to test before the probability of finding at least one bad one rises to more than .5? (You may have to use trial and error to solve this.)

To determine

To calculate: The number of bulbs that were tested by the manufacturer so that the probability of determining at least one bad bulb rises to more than 0.5 using trial and error method when a light bulb is chosen randomly by the manufacturer for testing and the probability that the bulb is found bad is 0.01.

Explanation

Given Information:

A light bulb is chosen randomly by the manufacturer for testing and the probability that the bulb is found bad is 0.01.

Formula Used:

If n is the number of trials and X is the number of successes, then the probability for particular value of X is given by:

P(X=x)=C(n,x)pxqnâˆ’x

Calculation:

Consider the probability of success is p=0.01.

Evaluate the probability P(Xâ‰¥1)â‰¥0.5 such that probability of finding at least one bad bulb rises to more than 0.5.

Evaluate the probability of P(Xâ‰¥1)â‰¥0.5,

P(Xâ‰¥1)â‰¥0.51âˆ’P(X=0)â‰¥0.5P(X=0)â‰¤0.5

Evaluate the value of n, number of trials by substituting the values in the formula P(X=x)=C(n,x)pxqnâˆ’x,

P(X=0)=C(n,0)(0.1)0(0.99)nâˆ’0

Then substitute the value of P(X=0)

C(n,0)(0.1)0(0.99)nâˆ’0â‰¤0.51Ã—1Ã—(0.99)nâ‰¤0.5(0.99)nâ‰¤0.5

Steps to calculate the number of trials using Excel Spread sheet as follows:

Step 1

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