two tollbooths are located at the entrance of an airport. at any given time the probability of a line at booth 1 is 0.77, the probability of a line at booth 2 is 0.62, and the probability of a line at both booths at the same time is 0.55. Draw a Venn diagram, and label the sections with numbers. Find the probability of a line: at neither booth at least at one booth at exactly one booth only at Booth 1

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12-12-2022
Mathematics

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two tollbooths are located at the entrance of an airport. at any given time the probability of a line at booth 1 is 0.77, the probability of a line at booth 2 is 0.62, and the probability of a line at both booths at the same time is 0.55. Draw a Venn diagram, and label the sections with numbers. Find the probability of a line: at neither booth at least at one booth at exactly one booth only at Booth 1

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AyushiJain10 AyushiJain10 · Answer 1 · 2022-12-21T10:38:59-05:00

The probability of a line only at Booth 1 is equal to the probability of a line at Booth 1 minus the probability of a line at both booths, which is equal to 0.77 - 0.55 = 0.22.

What is probability?

Probability is the study of the chances of occurrence of a result, which are obtained by the ratio between favorable cases and possible cases.

The probability of a line at neither booth is given by the area outside both circles, which is equal to 1 - 0.77 - 0.62 + 0.55 = 0.16.

The probability of a line at least at one booth is equal to the sum of the probabilities of a line at each booth plus the probability of a line at both booths, which is equal to 0.77 + 0.62 - 0.55 = 0.84.

The probability of a line at exactly one booth is equal to the probability of a line at Booth 1 plus the probability of a line at Booth 2 minus the probability of a line at both booths, which is equal to 0.77 + 0.62 - 2*0.55 = 0.24.

The probability of a line only at Booth 1 is equal to the probability of a line at Booth 1 minus the probability of a line at both booths, which is equal to 0.77 - 0.55 = 0.22.

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