An airline tracks data on its flight arrivals. Over the
past six months, 25 flights on one route arrived early,
150 arrived on time, 45 were late, and 30 were cancelled.
a. What is the probability that a flight is early? On
time? Late? Cancelled?
b. Are these outcomes mutually exclusive?
c. What is the probability that a flight is either early or
on time?
a. early- .1 on time- .6 late- .18 cancelled- .12
b. mutually exclusive
c. .7
To answer these questions, we need to calculate probabilities based on the given information.
a. Probability of a flight being early:
We are given that 25 flights arrived early out of a total of 25 + 150 + 45 + 30 = 250 flights. So, the probability of a flight being early is 25/250 = 0.10 or 10%.
Probability of a flight being on time:
We are given that 150 flights arrived on time out of a total of 250 flights. So, the probability of a flight being on time is 150/250 = 0.60 or 60%.
Probability of a flight being late:
We are given that 45 flights arrived late out of a total of 250 flights. So, the probability of a flight being late is 45/250 = 0.18 or 18%.
Probability of a flight being cancelled:
We are given that 30 flights were cancelled out of a total of 250 flights. So, the probability of a flight being cancelled is 30/250 = 0.12 or 12%.
b. To determine if the outcomes are mutually exclusive, we need to check if multiple outcomes can occur at the same time. In this case, a flight can only have one outcome: it can be either early, on time, late, or cancelled. Therefore, these outcomes are mutually exclusive.
c. To calculate the probability of a flight being either early or on time, we can add up the probabilities of these two outcomes. So, the probability that a flight is either early or on time is 0.10 (probability of being early) + 0.60 (probability of being on time) = 0.70 or 70%.