Question

In order to drive from your home to the store, there has to be at least one operating route. Once a bridge is closed on a route, that route is no longer operating. The probability that bridge 1 is open is 0.8, bridge 2 is 0.93, bridge 3 is 0.9, bridge 4 is 0.92, and bridge 5 is 0.94. What is the probability you can drive to the store? Answer to 3 decimals.

Answer 1

The probability of driving to the store is 0.969

Explanation:

The remaining part of the question is attached

Solution

There are only two possible ways –

a) Route comprising of bridges 123

b) Route comprising of bridge 45

Probability of success while traveling through Route 123 = P(Bridge 1 open) x P(Bridge 2 open) x P(Bridge 3 open)

= 0.9 x 0.92 x 0.91

= 0.75348

P(Route 123 is closed) = 1 - 0.75348 = 0.24652

Probability of success while traveling through Route 45 =

P(Bridge 4 open) x P(Bridge 5 open)

= 0.94 x 0.93

= 0.8742

P(Route 45 is closed) = 1 - 0.8742 = 0.1258

To travel to store, atleast one route from 123 and 45 should be open.

Probability that you can drive to store :

= P(atleast one route from 123 and 45 is open)

= 1 - P(Both routes 123 and 45 are closed)

= 1 - P(123 is closed)*P(45 is closed)

= 1 - 0.24652*0.1258

= 1 - 0.031012216

= 0.968987784

~ 0.969