Question

By rewriting the formula for the Multiplication​ Rule, you can write a formula for finding conditional probabilities. The conditional probability of event B​ occurring, given that event A has​ occurred, is P (B A) = P (A and B) P (A).
Use the information below to find the probability that a flight arrives on time given that it departed on time.
1. The probability that an airplane flight departs on time is 0.91.
2. The probability that a flight arrives on time is 0.86.
3. The probability that a flight departs and arrives on time is 0.81.

Answer 1

Answer:

89.01% probability that a flight arrives on time given that it departed on time.

Step-by-step explanation:

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: Departing on time

Event B: Arriving on time.

The probability that a flight departs and arrives on time is 0.81.

This means that $P(A \cap B) = 0.81$

The probability that an airplane flight departs on time is 0.91.

This means that $P(A) = 0.91$

Find the probability that a flight arrives on time given that it departed on time.

$P(B|A) = \frac{0.81}{0.91} = 0.8901$

89.01% probability that a flight arrives on time given that it departed on time.