Question

Suppose that Jamal can choose to get home from work by taxi or bus.

• When he chooses to get home by taxi, he arrives home after 7 p.m.
8 percent of the time.

• When he chooses to get home by bus, he arrives home after 7 p.m.
15 percent of the time.

• Because the bus is cheaper, he uses the bus 60 percent of the time.

What is the approximate probability that Jamal chose to get home from work by bus, given that he arrived home after 7 p.m.?

A 0.09
B 0.14
C 0.60
D 0.74

I know the answer, but please explain how to do the problem.

Answer 1

Jamal has a 60% chance of taking the bus. Out of the times Jamal takes the bus, he arrives from work after 7 PM 15% of the time.

Two criteria have to be met in this problem, so the probabilities will be multiplied together.

Convert the percentages into decimal form by dividing each percentage by 100:

$60 \div 100 = 0.6$
$15 \div 100 = 0.15$

Multiply these decimals together to find the experimental probability:

$0.6 \times 0.15 = 0.09$

Jamal has a 0.09 (9%) chance of arriving home after 7 PM while taking the bus.