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 Upper P left parenthesis Upper B vertical line Upper A right parenthesis equals StartFraction Upper P left parenthesis Upper A and Upper B right parenthesis Over Upper P left parenthesis Upper A right parenthesis EndFraction . 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 0.86.

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 2 nothing. ​(Round to the nearest thousandth as​ needed.)

Answer 1

P(flight departed on time | it arrives on time) = P(flight departs and arrives on time) / P(flight arrives on time)

                                                                       = 0.82 / 0.86

                                                                       = 0.953