Question

14. A company uses many different delivery

Answer 1

Answer:

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

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: 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

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

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

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