Question

Finding Complements. In Exercises 5–8, find the indicated complements.

Flights According to the Bureau of Transportation, 80.3% of American Airlines flights arrive on time. What is the probability of randomly selecting an American Airlines flight that does not arrive on time?

Short answer

The probability of selecting a flight that does not arrive on time is equal to 0.197.

Step-by-step solution

Given information

In a survey, 80.3% of American airlines’ flights arrive on time.

Define complementary events

Complementary events: Consider A as the event of occurrence in an experiment. Then, $\overline{A}$denoting the non-occurrence of the same event are complementary events

The sum of probabilities for complementary events is always 1.

$P\left(A\right)+P\left(\overline{A}\right)=1$

Compute the probability for the complement of the given event

Let A be the event of selecting a flight that arrives on time.

Then,$\overline{A}$ be the event of selecting a flight that does not arrive on time.

The probability values are obtained by dividing the percentages by 100.

The probability of selecting a flight that does not arrive on time is:

$$\begin{gathered} P\left(\overline{A}\right)=1-P\left(A\right) \\ =1-\frac{80.3}{100} \\ =\frac{19.7}{100} \\ =0.197 \end{gathered}$$

Therefore, the probability of selecting a flight that does not arrive on time is 0.197.