SOLUTION: Suppose there is a 69 percent chance that there will be traffic congestion on Bridge A, a 57 percent chance there will be traffic congestion on bridge B, and a 45 percent chance th

Algebra ->  Probability-and-statistics -> SOLUTION: Suppose there is a 69 percent chance that there will be traffic congestion on Bridge A, a 57 percent chance there will be traffic congestion on bridge B, and a 45 percent chance th      Log On


   

Question 267846: Suppose there is a 69 percent chance that there will be traffic congestion on Bridge A, a 57 percent chance there will be traffic congestion on bridge B, and a 45 percent chance there will be traffic on both bridges. what is the probability that there will be traffic congestion on AT LEAST one bridge?
Answer by stanbon(75887) About Me  (Show Source):
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Suppose there is a 69 percent chance that there will be traffic congestion on Bridge A, a 57 percent chance there will be traffic congestion on bridge B, and a 45 percent chance there will be traffic on both bridges. what is the probability that there will be traffic congestion on AT LEAST one bridge?
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P(A jam) = 0.69
P(B jam) = 0.57
P(A and B) = 0.45
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P(jam on at least one) = 1 - P(jam on none)
P(jam on none) = P(A' and B')
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P(A' and B') = P(A') + P(B') - P(A' or B')
P(A' or B') = 1-P(A and B)
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So P(A' and B') = 0.31 + 0.43 -[1-0.45]
= 0.74 - 0.55
= 0.19
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Therefore P(jam on at least one) = 1-0.19 = 0.81
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cheers,
Stan H.
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P(jam on at least one) = 1 - P(jam on none)