An airline has 87% of its flights depart on schedule. It has 68% of its flights depart and arrive on schedule. Find the probability that a flight that departs on schedule also arrives on schedule. Round the answer to two decimal places. (1 point) Responses 0.59 0.59 0.85 0.85 0.78 0.78 1.55
To find the probability that a flight that departs on schedule also arrives on schedule, we need to use the formula for conditional probability.
Let A be the event that a flight departs on schedule, and let B be the event that a flight arrives on schedule. We want to find P(B|A), the probability that a flight arrives on schedule given that it departs on schedule.
We know that:
P(A) = 0.87 (probability that a flight departs on schedule)
P(A and B) = 0.68 (probability that a flight departs and arrives on schedule)
The formula for conditional probability is given by:
P(B|A) = P(A and B) / P(A)
Substitute the known probabilities into the formula:
P(B|A) = 0.68 / 0.87
P(B|A) ≈ 0.78
Therefore, the probability that a flight that departs on schedule also arrives on schedule is approximately 0.78, rounded to two decimal places.
Correct answer: 0.78