Question

Of the travelers arriving at a small airport, 60% fly on major airlines, 20% fly on privately owned planes, and the remainder fly on commercially owned planes not belonging to a major airline. Of those traveling on major airlines, 40% are traveling for business reasons, whereas 70% of those arriving on private planes and 80% of those arriving on other commercially owned planes are traveling for business reasons. Suppose that we randomly select one person arriving at this airport.

What is the probability that the person is traveling on business?

Answer 1

Answer: 54% or 0.54

Step-by-step explanation:

The probability that the person is travelling on business is the expected value of the various probabilities that they are travelling on business.

= (Percentage using major airlines * percentage using major airlines to travel for business) + (Percentage using private * percentage using private airlines to travel for business) + (Percentage using commercial * percentage using commercial airlines to travel for business)

= (60% * 40%) + (20% * 70%) + ( (100% - 60% - 20%) * 80%)

= 24% + 14% + 16%

= 54%