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A First Course in Probability | 9th Edition | ISBN: 9780321794772 | Authors: Sheldon Ross
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(a) In 3.66b, find the probability that a current flows

Chapter 3, Problem 16STE

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QUESTION:

Problem 16STE

(a) In Problem 3.66b, find the probability that a current flows from A to B, by conditioning on whether relay 1 closes.

(b) Find the conditional probability that relay 3 is closed given that a current flows from A to B.

Questions & Answers

QUESTION:

Problem 16STE

(a) In Problem 3.66b, find the probability that a current flows from A to B, by conditioning on whether relay 1 closes.

(b) Find the conditional probability that relay 3 is closed given that a current flows from A to B.

ANSWER:

Step 1 of 2

(a)

We are asked to find the probability that a current flows from  to  by conditioning on whether relay 1 closes.

Let  be the event the  relay is closed (so that current can flow through that connection) and let  be the current flows between  and

If relay 1 is closed then the event current flows is

If on the other hand relay 1 is open the event current flows is

Thus the probability that current flow is using total probability rule,

Since all relays are independent, we can write using addition rule of probability

By independence, each of term in the above can be expanded in terms of products of  using these two results we find

 

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