1.5.7 Consider the network given in Figure 1.66 with three switches. Suppose that the switches operate independently of each other and that switch 1 allows a message through with probability 0.88, switch 2 allows a message through with probability 0.92, and switch 3 allows a message through with probability 0.90. What is the probability that a message will find a route through the network?

A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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1.5.7 Consider the network given in Figure 1.66 with three
switches. Suppose that the switches operate independently
of each other and that switch 1 allows a message through
with probability 0.88, switch 2 allows a message through
with probability 0.92, and switch 3 allows a message
through with probability 0.90. What is the probability that
a message will find a route through the network?
Transcribed Image Text:1.5.7 Consider the network given in Figure 1.66 with three switches. Suppose that the switches operate independently of each other and that switch 1 allows a message through with probability 0.88, switch 2 allows a message through with probability 0.92, and switch 3 allows a message through with probability 0.90. What is the probability that a message will find a route through the network?
1.5 PROBABILITIES OF EVENT INTERSECTIONS
49
FIGURE 1.66
1
Switch diagram
0,88
0.92
?
3
0.90
Transcribed Image Text:1.5 PROBABILITIES OF EVENT INTERSECTIONS 49 FIGURE 1.66 1 Switch diagram 0,88 0.92 ? 3 0.90
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