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)=\frac{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. 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 0.84. the probability that a flight arrives on time given that it departed on time is. (round to the nearest thousandth as needed.)

Explanation:

Step1: Identify the values

Let \(A\) be the event that the flight departs on time and \(B\) be the event that the flight arrives on time. We are given \(P(A)=0.91\), \(P(A\cap B) = 0.84\)

Step2: Apply the conditional - probability formula

The formula for conditional probability is \(P(B|A)=\frac{P(A\cap B)}{P(A)}\)

Substitute the values: \(P(B|A)=\frac{0.84}{0.91}\)

Step3: Calculate the value

\(P(B|A)=\frac{0.84}{0.91}\approx0.923\)

Answer:

\(0.923\)