The following connected road operates if and only if there is a path of function

Question

The following connected road operates if and only if there is a path of functional tolls from left to right. The probability of each toll functioning during an emergency evacuation is shown in the figure. In addition, P(Holland) = 0.9 and P(Lincoln) = 0.92. Assume all the tolls function independent of each other except Holland and Lincoln tunnels. If P(Holland ? Lincoln) = 0.88, what is the probability that you can escape to New Jersey from your newly developed project in Queens during a Hurricane?

Explanation / Answer

P(Holland/Lincoln)=0.88

You can escape if both gates are open,hence=P(A intersection B)=P(B) x P(A/B)=0.92 x 0.88=0.8096

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