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 \mid a) = \frac{p(a \text{ and } b)}{p(a)}\\). use the information below to find the probability that a flight departed on time given that it arrives on time.

the probability that an airplane flight departs on time is 0.91.
the probability that a flight arrives on time is 0.89.
the probability that a flight departs and arrives on time is 0.82.

the probability that a flight departed on time given that it arrives on time is .
(round to the nearest thousandth as needed.)

Explanation:

Define events and probabilities

Using the Conditional Probability Notation knowledge point

$$
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$$

Apply conditional probability formula

Using the Conditional Probability Notation knowledge point

$$
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$$

Calculate and round the final value

Using the Conditional Probability Notation knowledge point

$$
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$$

Answer:

The probability that a flight departed on time given that it arrives on time is <blank>0.921</blank>
(Round to the nearest thousandth as needed.)