Question

Job Elimination In the past year, 15% of businesses have eliminated jobs. If 3 businesses are selected at random, find the probability that at least 1 has eliminated jobs during the last year. Round your answer to at least three decimal places. Do not round your intermediate calculations.

Answer 1

0.386 or 38.6%

To find the probability that at least one of the three randomly selected businesses has eliminated jobs in the past year, we can use the complement rule. The complement of "at least one has eliminated jobs" is "none of them has eliminated jobs." The probability of this happening for each business is 1−0.15 (because 15% have eliminated jobs), and since the events are independent, we multiply the probabilities.

The probability of none of the three businesses eliminating jobs is given by:

P(none eliminated) =
`(1-0.15)^(3)`

Now, the probability of at least one business eliminating jobs is the complement of the above probability:

P(at least one eliminated)=1−P(none eliminated)

Let's calculate this:

P(at least one eliminated)= 1−
`(1-0.15)^(3)` = 0.385875

So, the probability that at least one of the three randomly selected businesses has eliminated jobs in the past year is approximately 0.386 or

38.687% (rounded to three decimal places).