You take a trip by air that involves three independent flights. If there is an 85% chance each specific leg of the trip is on time, what is the probability all three flights arrive on time? (Round your answer to 3 decimal places.)
To find the probability that all three flights arrive on time, we can use the principle of multiplication.
Since each leg of the trip is independent, the probability of all three flights arriving on time is given by the product of the probabilities of each leg being on time.
The probability of one leg being on time is 85%, which can be written as 0.85 in decimal form.
So, to find the probability of all three flights arriving on time, we need to multiply 0.85 by itself three times, as there are three independent flights:
P(all three flights on time) = 0.85 * 0.85 * 0.85 = 0.614125
Rounding this to three decimal places, the probability that all three flights arrive on time is approximately 0.614.