Question

In: Statistics and Probability

The City of San Francisco has two bridges, Golden Gate Bridge and Bay Bridge. Assume these...

The City of San Francisco has two bridges, Golden Gate Bridge and Bay Bridge. Assume these two bridges are designed to survive during earthquakes with magnitude of less than 7 Richter with the probabilities of 0.95 and 0.98. What is the probability that at least one of these two bridges collapse facing an earthquake with magnitude of over 7 Richter?

Solutions

Expert Solution

Given,

Probability that Golden Gate Bridge survive(does not collapse) facing an earthquake with magnitude of over 7 Richter = 0.95

Probability that Bay Bridge survive(does not collapse) facing an earthquake with magnitude of over 7 Richter = 0.98

Probability that at least one of these two bridges collapse facing an earthquake with magnitude of over 7 Richter

= 1 - Probability that both these two bridges survive(does not collapse) facing an earthquake with magnitude of over 7 Richter

Probability that both these two bridges survive(does not collapse) facing an earthquake with magnitude of over 7 Richter

= Probability that (Golden Gate Bridge survive(does not collapse) facing an earthquake with magnitude of over 7 Richter and Bay Bridge survive(does not collapse) facing an earthquake with magnitude of over 7 Richter)

= Probability that (Golden Gate Bridge survive(does not collapse) facing an earthquake with magnitude of over 7 Richter x

Probability that  Bay Bridge survive(does not collapse) facing an earthquake with magnitude of over 7 Richter

= 0.95 x 0.98 = 0.931

Probability that at least one of these two bridges collapse facing an earthquake with magnitude of over 7 Richter

= 1 - Probability that both these two bridges survive(does not collapse) facing an earthquake with magnitude of over 7 Richter = 1- 0.931 = 0.069

Probability that at least one of these two bridges collapse facing an earthquake with magnitude of over 7 Richter = 0.069

orchestra answered 2 years ago
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