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Question Video: Determining the Probability of Complement of an Event Mathematics • 10th Grade

The table shows the percentage of flights which arrived on time at several airports. If a flight due to land at Baltimore Airport (MD) is randomly selected, determine the probability that the flight will NOT arrive on time, expressing your answer as a percent, a decimal, and a fraction.

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Video Transcript

The table shows the percentage of flights which arrived on time at several airports. If a flight due to land at Baltimore Airport in Maryland is randomly selected, determine the probability that the flight will not arrive on time, expressing your answer as a percent, a decimal, and a fraction.

In this question, we are given the percentage of flights which arrive on time at five different airports across the United States. We are interested in a flight that is due to land at Baltimore Airport. From the table, we see that 60 percent of the flights here arrive on time. This means that the probability that a flight arrives on time at Baltimore Airport is 60 percent. We are asked to calculate the probability that a flight will not arrive on time.

An event not occurring is known as the complement of the event, and this is denoted 𝐴 bar or 𝐴 prime. We know that the probability of 𝐴 bar is equal to one minus the probability of 𝐴. And when dealing with percentages to calculate the probability of the complement, we subtract the probability of the event from 100 percent. The probability that a flight will not arrive on time in Baltimore is therefore equal to 100 percent minus 60 percent. This is equal to 40 percent.

We are also asked to write our answer as a decimal. And we know that to convert from a percent to a decimal, we divide by 100 as percentages are out of 100. 40 divided by 100 is 0.4. Finally, we are asked to express our answer as a fraction, and this is equal to 40 over 100. Dividing the numerator and denominator by 10, this simplifies to four over 10 or four-tenths. We can simplify this one stage further by dividing the numerator and denominator by two, giving us an answer of two-fifths.

The probability that a flight due to arrive at Baltimore Airport will not arrive on time is 40 percent, 0.4, or two-fifths. For any question involving probability, we can express our answer as a percent, a decimal, or a fraction.

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