Driving safely A. Suppose Grandpa can enter a busy street from a small side stre

Question

Driving safely

A. Suppose Grandpa can enter a busy street from a small side street or he can enter the busy street at a road with a stop light. Presume the probability of entering safely from the small side street one time is .9991. Over the next 10 years of driving, Grandpa will enter the busy street from the side street 32,800 times. Presuming each entrance on to the busy street is independent, find the probability Grandpa will enter safely by the side street over the next 10 years.

B. This makes you quite concerned. You notice if Grandpa drove down two blocks, he could enter the busy street from a stop light. The probability of entering the busy street safely from the stop light one time is .999994. Presuming each of the 32,800 times Grandpa will be entering the busy street is independent, find the probability Grandpa will enter safely from the stop light over the next ten years.

Explanation / Answer

Answer:

Probability of entering safely from the small side one time = 0.9991

Total number of times Grandpa will enter the busy street from the side street in next 10 years = 32800

Each entrance is independent, probability Grandpa will enter safely by the side street over next 10 years = (0.9991)32800 = 1.49*10-13

The probability of entering the busy street safely from the stop light one time = .999994  

Total number of times Grandpa will enter the busy street safely from the stop light = 32800

Probability Grandpa will enter safely from the stop light over the next ten years = (0.999994)32800 =0.82135

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