Dystopia county has three bridges. in the next year, the elder bridge has a 16% chance of collapse, the younger bridge has a 4% 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.)

The answer is 0.3629

Step-by-step explanation:

Let E represent the elder bridge

Let Y represent the younger bridge

Let A represent the ancient bridge

The chance that the elder bridge will collapse next year is 16%

Pr(E) = 16%

= 0.16

The chance that the elder bridge will not collapse next year is Pr(E')

Pr(E')= 1 – 0.16

= 0.84

The chance that the younger bridge will collapse next year is 4%

Pr(Y) = 4%

= 0.04

The chance that the younger bridge will not collapse next year is Pr(Y')

Pr(Y')= 1 – 0.04

= 0.96

The chance that the ancient bridge will collapse next year is 21%

Pr(A) = 21%

= 0.21

The chance that the ancient bridge will not collapse next year is Pr(A')

Pr(A')= 1 – 0.21

= 0.79

The probability that exactly one of the bridge s will collapse next year is

1 – (Pr(E') n Pr(Y') n Pr(A'))

= 1 – (0.84*0.96*0.79)

= 1 – 0.637056

= 0.362944

= 0.3629(to 4 decimal place)