Consider a system of water flowing through valves from A to B. (See the accompanying

Chapter 3, Problem 3.4

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QUESTION:

Consider a system of water flowing through valves from A to B. (See the accompanying diagram.) Valves 1, 2, and 3 operate independently, and each correctly opens on signal with probability .8. Find the probability distribution for Y , the number of open paths from A to B after the signal is given. (Note that Y can take on the values 0, 1, and 2.) A B 1 2 3

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QUESTION:

Consider a system of water flowing through valves from A to B. (See the accompanying diagram.) Valves 1, 2, and 3 operate independently, and each correctly opens on signal with probability .8. Find the probability distribution for Y , the number of open paths from A to B after the signal is given. (Note that Y can take on the values 0, 1, and 2.) A B 1 2 3

ANSWER:

Step 1 of 4

Let the sample events be

A-valve 1 opens, B-valve 2 opens, C-valve 3 opens.

We need to find   and .

The probability distribution is .

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