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

Please explain how D is correct.

Answer 1

It is D

Explanation:

First you want to create a tree diagram.

< After 7 (.8)

<

> (.40) Taxi < Before 7 (.92)

>

> (.60) Bus < After 7 (.15)

<

< Before 7 (.85

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

**Given**

P(goes to work with bus) | (after 7)

work from right to left.

After 7 = .12 ---> this is because working from right to left gave no specifics so you have to include all of the after 7's so you multiply them.

Goes to work with bus = .60

(.60 | .15) = To figure this out plug into probability formula.

so that P(B|A) = P(B) x P(A) which will equal .09

Now plug into the Dependent Formula which is P(AandB) = P(A) x P(B|A)

And plug in answers you got.

P(.09) = P(.12) x P(B | A) <--- Now get this by it self.

.09 / .12 = .75

.75 = P(B | A)