You take a trip by air that involves three independent flights. If there is an 67% 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.)
Probability=
If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.
.67^3 = ?
To find the probability that all three flights arrive on time, we can multiply the probabilities of each individual flight being on time since the flights are independent events.
Given that there is a 67% chance (or 0.67 probability) for each specific leg of the trip to be on time, the probability of a leg being on time is 0.67.
Therefore, the probability of all three flights arriving on time can be calculated as:
Probability = 0.67 * 0.67 * 0.67
Simplifying this expression, we get:
Probability = 0.67^3
Calculating the value, we find:
Probability = 0.67 * 0.67 * 0.67 = 0.300763
Therefore, the probability that all three flights arrive on time is approximately 0.301 (rounded to 3 decimal places).