. a commuter must pass through four traffic lights on her way to work. for each light, the probability that it is green when she arrives is 0.7. assuming the lights are independent a. what is the probability that all four are green? b. the commuter goes to work five days per week. what is the probability that all four will be green on exactly three days?

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20-12-2022
Mathematics

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. a commuter must pass through four traffic lights on her way to work. for each light, the probability that it is green when she arrives is 0.7. assuming the lights are independent a. what is the probability that all four are green? b. the commuter goes to work five days per week. what is the probability that all four will be green on exactly three days?

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abhinavjh321 abhinavjh321 · Answer 1 · 2022-12-25T00:10:53-05:00

The probability that all four traffic lights are green when the commuter arrives is 0.2401 and The probability that all four will be green on exactly three days is 0.2079.

A. The probability that all four traffic lights are green when the commuter arrives is calculated by multiplying the probability of each light being green by itself 4 times: 0.2401.

B. To calculate the probability that all four are green on exactly three days, we first have to calculate the probability of all four lights being green on any one day, which is 0.2401. Then, we multiply 0.2401 by the number of days the commuter goes to work (5) and subtract this from 1 (the probability of all four being green on all five days). This gives us the probability of all four being green on exactly three days, which is 0.2079.

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