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Through several hundred trials, on any given commute on a particular street road, the probability that...

Through several hundred trials, on any given commute on a particular street road, the probability that a taxi car needs to legally stop at a traffic light is approximately 45%. If all traffic lights in a city are independent of one another, what is the probability that a randomly selected taxi driver will be able to legally drive through at-most five traffic lights until they need to stop at the traffic light?

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Answer #1

probability that a taxi car needs to stop, p = 0.45

The car will be stopped at 6th signal.

Required probability = 0.45 + (1-0.45)*0.45 + (1 - 0.45)^2 * 0.45 + (1 - 0.45)^3 * 0.45 + (1 - 0.45)^4 * 0.45 + (1 - 0.45)^5 * 0.45
= 0.9723

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