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A First Course in Probability | 9th Edition | ISBN: 9780321794772 | Authors: Sheldon Ross
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A type C battery is in working condition with probability

Chapter 3, Problem 11STE

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QUESTION:

Problem 11STE

A type C battery is in working condition with probability .7, whereas a type D battery is in working condition with probability .4. A battery is randomly chosen from a bin consisting of 8 type C and 6 type D batteries.

(a) What is the probability that the battery works?

(b) Given that the battery does not work, what is the conditional probability that it was a type C battery?

Questions & Answers

QUESTION:

Problem 11STE

A type C battery is in working condition with probability .7, whereas a type D battery is in working condition with probability .4. A battery is randomly chosen from a bin consisting of 8 type C and 6 type D batteries.

(a) What is the probability that the battery works?

(b) Given that the battery does not work, what is the conditional probability that it was a type C battery?

ANSWER:

Step 1 of 3

Let the probability for C type battery is , and

The probability for D type BAttery is

Also, we have and

The number of C type batteries is 8, the number of D type batteries is 6, and total number of batteries are 14.

Here our goal is:

a). We need to find the probability that the battery works.

b). We need to find the conditional probability that it was a type C battery.

 

Step2 of 3

a).

The probability that the battery works is:

     

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