Question

14. A company uses many different delivery

services. The probability that any given parcel
will be sent by the ABC Speedy Delivery Service
is 0.71. The probability that the parcel will arrive
on time given the ABC Speedy Delivery
Company was used is 0.93. If a parcel is
randomly selected, find the probability that it will
be sent with the ABC Speedy Delivery Company
and arrive on time.

Answer 1

0.6603 = 66.03% probability that it will be sent with the ABC Speedy Delivery Company and arrive on time.

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: Sent by ABC Speedy Delivery Service.

Event B: Arrived on time.

The probability that any given parcel will be sent by the ABC Speedy Delivery Service is 0.71.

This means that
`P(A) = 0.71`

The probability that the parcel will arrive on time given the ABC Speedy Delivery Company was used is 0.93.

This means that
`P(B|A) = 0.93`

Find the probability that it will be sent with the ABC Speedy Delivery Company and arrive on time.

This is
`P(A \cap B)`. So

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

`P(A \cap B) = P(B|A)*P(A) = 0.93*0.71 = 0.6603`

0.6603 = 66.03% probability that it will be sent with the ABC Speedy Delivery Company and arrive on time.