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
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] 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 [tex]P(A \cap B) = 0.15[/tex]
More than 2 lbs:
15% of 20%(UPS)
93% of 80%(Not delivered by UPS). So
[tex]P(A) = 0.15*0.2 + 0.93*0.8 = 0.774[/tex]
a. What is the probability that a package is delivered by UPS if it weighs 2 lbs or more
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.15}{0.774} = 0.1938[/tex]
0.1938 = 19.38% probability that a package is delivered by UPS if it weighs 2 lbs or more
