Question

Dystopia county has three bridges. In the next year, the Elder bridge has a 15% chance of collapse, the Younger bridge has a 6% chance of collapse, and the Ancient bridge has a 24% 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.)

Answer 1

Using probabilities of independent events, it is found that there is a 0.3377 = 33.77% probability that exactly one of these bridges will collapse in the next year.

When multiple events are independent, the probability of all happening is the multiplication of the probabilities of each happening.

In this problem, three outcomes result in exactly one bridge collapsing.

• The first collapses, with 0.15 probability, and neither of the last two collapse, with 0.94 and 0.76 probability.
• The second collapses, with 0.06 probability, while neither the first or the third collapse, with 0.85 and 0.76 probability.
• The third collapses with 0.24 probability, while neither of the first two collapse, with 0.85 and 0.94 probability.

The collapse of the bridges are independent, which means that the probability of exactly one collapsing is:

$p = 0.15(0.94)(0.76) + 0.06(0.85)(0.76) + 0.24(0.85)(0.94) = 0.3377$

0.3377 = 33.77% probability that exactly one of these bridges will collapse in the next year.

A similar problem is given at https://brainly.com/question/24907195