Question

An airline estimates that 90% of its eastbound flights arrive on time and 72% of its westbound flights arrive on time. This morning, 42% of the airline’s schedule is westbound flights. If a flight is chosen at random, what is the probability that the flight does not arrive on time? Write your answer as a percent rounded to the nearest tenth.

Answer 1

The probability, that a flight does not arrive on time is 18.4%

Explanation:

Here we have that;

The percentage of the Eastbound flight that arrive on time = 90%

The percentage of the Westbound flight that arrive on time = 72%

The percentage of Westbound flights the present morning = 42%

Therefore, the percentage of Eastbound flights the present morning = 100% - 42% = 58%

Hence the probability, p, that a flight will arrive on time this morning is given as follows

0.9 × 0.58 + 0.72 × ×0.42 = 0.816

Hence the probability, q, that a flight does not arrive on time = 1 - p

Which gives, q = 1 - 0.816 = 0.184

To convert back to percentage, we multiply by 100 hence;

0.184 × 100 = 18.4%

The probability, that a flight does not arrive on time = 18.4%.

Answer 2

Probability that the flight doesn't arrive on time = 0.2 (to the nearest tenth)

Explanation:

90% of the eastbound flights arrive on time, i.e. Pe = 0.9

10% of the eastbound flights do not arrive on time, Qe =1 - 0.9 = 0.1

72% of the westbound flights arrive on time, i.e. Pw = 0.72

28% of the westbound flights do not arrive on time, Qw =1 - 0.72 = 0.28

42% of the airline schedule this morning is westbound (i.e 58% is eastbound)

If a flight is chosen at random:

Probability that it is a westbound flight and it does not arrive on time = 0.28 * 0.42 = 0.1176

Probability that it is an eastbound flight and it does not arrive on time = 0.1 * 0.58 = 0.058

Probability that the flight doesn't arrive on time = 0.1176 + 0.058

Probability that the flight doesn't arrive on time = 0.1756

Probability that the flight doesn't arrive on time = 0.2 (to the nearest tenth)