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Read the story. Roger works as a gate agent for Nimbus Airlines. In his experience, every Nimbus flight has a 15% chance of being overbooked. If 10 Nimbus flights are scheduled to take off tonight, how likely is it that none of the flights will be overbooked? Roger simulates the situation by using a computer to randomly generate 10 numbers from 1 to 20. Each time a 1, 2, or 3 appears, it represents an overbooked flight. This table shows the results of 200 trials: Number of times a 1, 2, or 3 appears 0 1 2 3 4 5 6 7 8 9 10 Number of trials 40 68 55 26 9 2 0 0 0 0 0 Based on Roger's results, what is the probability that none of the flights will be overbooked? %



Answer :

To find the probability that none of the flights will be overbooked based on Roger's results, we need to calculate the proportion of trials where the number of times a 1, 2, or 3 appears is 0.

From the table provided, we can see that there are 40 trials where the number of times a 1, 2, or 3 appears is 0.

To find the total number of trials, we sum up all the numbers in the "Number of trials" column:

Total number of trials = 40 + 68 + 55 + 26 + 9 + 2 + 0 + 0 + 0 + 0 + 0 = 200

Therefore, the probability that none of the flights will be overbooked is:

Probability

=

Number of trials where no overbooked flights

Total number of trials

×

100

Probability=

Total number of trials

Number of trials where no overbooked flights

​

×100

Probability

=

40

200

×

100

Probability=

200

40

​

×100

Probability

=

1

5

×

100

Probability=

5

1

​

×100

Probability

=

20

%

Probability=20%

So, based on Roger's results, the probability that none of the flights will be overbooked is 20%.

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