Question

Suppose that out of 20% of all packages from Amazon are delivered by UPS. 15% of the packages that are delivered by UPS weighs 2 lbs or more. Also, 7% of the packages that are not delivered by UPS weighs less than 2 lbs. a. What is the probability that a package is delivered by UPS if it weighs 2 lbs or more

Answer 1

0.1938 = 19.38% probability that a package is delivered by UPS if it weighs 2 lbs or more

Explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

`P(B|A) = (P(A \cap B))/(P(A))`

In which

P(B|A) is the probability of event B happening, given that A happened.

`P(A \cap B)` is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: It weighs 2 lbs or more

Event B: Delivered by UPS

15% of the packages that are delivered by UPS weighs 2 lbs or more.

This means that
`P(A \cap B) = 0.15`

More than 2 lbs:

15% of 20%(UPS)

93% of 80%(Not delivered by UPS). So

`P(A) = 0.15*0.2 + 0.93*0.8 = 0.774`

a. What is the probability that a package is delivered by UPS if it weighs 2 lbs or more

`P(B|A) = (P(A \cap B))/(P(A)) = (0.15)/(0.774) = 0.1938`

0.1938 = 19.38% probability that a package is delivered by UPS if it weighs 2 lbs or more