This question is a case of conditional probability and thus it can be solved by the use of the formula:
[tex] P(B|A)=\frac{P(A\cap B)}{P(A)} [/tex]
Now, in our case, let A be the event that a flight departs on schedule and
let B be the event that a flight arrives on schedule.
Thus, from the given data, we know that: [tex] P(A) = 0.82 [/tex] and [tex] P(A \cap B) = 0.65 [/tex]
Thus, the conditional probability that a flight that departs on schedule also
arrives on schedule will be:
[tex] P(B | A) =\frac{ P(B \cap A)}{P(A)}=\frac{0.65}{0.82}\approx0.7927 [/tex]
Therefore, when expressed as a percentage, rounded to two places of decimal, the required probability is 79.27%.
