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

Answer:

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

Step-by-step explanation:

Conditional Probability

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

$P(B|A) = \frac{P(A \cap B)}{P(A)}$

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

$P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.15}{0.774} = 0.1938$

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