A survey of 500 top Canadian companies reported what the companies' hiring outlook was for the next 18 months as well as the general company outlook for the economy over the same period of time. Given that a randomly selected company has a favourable forecast, what is the probability that it plans to cut jobs during the next 18 months?
A) 25/500
B) 25/175
C) 125/175
D) 175/500

Question

A survey of 500 top Canadian companies reported what the companies' hiring outlook was for the next 18 months as well as the general company outlook for the economy over the same period of time.  Given that a randomly selected company has a favourable forecast, what is the probability that it plans to cut jobs during the next 18 months?
A) 25/500 
B) 25/175 
C) 125/175 
D) 175/500

Quizplus · Accepted Answer

We need to use Bayes' theorem to solve the problem. Let F be the event of a favourable forecast, and J be the event of job cuts. We want to find P(J|F). Bayes' theorem tells us that:
P(J|F) = P(F|J) * P(J) / P(F)
We know that P(J) = 25/500 since 25 companies plan to cut jobs. We also know that P(F) = (175+25)/500 = 0.4 since there are a total of 175+25 = 200 companies with favourable forecasts. It remains to find P(F|J).
To find P(F|J), we need to think about the conditional probability of a favourable forecast given that a company is planning to cut jobs. It seems reasonable to assume that companies planning to cut jobs are generally pessimistic about the economy and therefore less likely to have a favourable forecast. So we might guess that P(F|J) is low. In particular, we might guess that P(F|J) = 0.1, meaning that only 10% of the companies planning to cut jobs have a favourable forecast.
Using this value, we get:
P(J|F) = 0.1 * (25/500) / 0.4 = 0.0125
So the probability of a company with a favourable forecast planning to cut jobs is 0.0125, or 25/200, which simplifies to 25/175.

A Survey of 500 Top Canadian Companies Reported What the Companies