Dystopia county has three bridges. In the next year, the Elder bridge has a 13% chance...

Dystopia county has three bridges. In the next year, the Elder bridge has a 13% chance of collapse, the Younger bridge has a 7% chance of collapse, and the Ancient bridge has a 21% chance of collapse. What is the probability that exactly one of these bridges will collapse in the next year? (Round your final answer to four decimal places. Do not round intermediate calculations.)

Solutions

Expert Solution

Given that the county has three bridges, the Elder bridge, the Younger bridge and the Ancient bridge.

The probability that the Elder bridge will collapse is given =0.13

The probability that the Younger bridge will collapse is given =0.07

The probability that the Ancient bridge will collapse is given =0.21

To calculate the probability that only one bridge will collapse we need to consider the probability of one bridge collapsing and the probability of other two bridge not collapsing.

So, the probability can be calculated as:

Probability of the Elder bridge collapsing x Probability of the Younger bridge Not collapsing x Probability of the Ancient bridge Not collapsing

+ Probability of the Elder bridge Not collapsing x Probability of the Younger bridge collapsing x Probability of the Ancient bridge Not collapsing

+ Probability of the Elder bridge Not collapsing x Probability of the Younger bridge Not collapsing x Probability of the Ancient bridge collapsing

This is equal to:

=0.13x0.93x0.79 + 0.87x0.07x0.79 + 0.87x0.93x0.21

= 0.095511 + 0.048111 + 0.169911

= 0.3135

Thus, the required probability is 0.3135.

orchestra answered 1 year ago

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