Respuesta :
Answer:
We are given that During each trip his car has a tire failure in each 100-mile stretch with a probability of 0.05.
Probability of failure = 0.05
Probability of success = 1- 0.05 = 0.95
a) What is the probability that the first change of tire occurred 300 miles from his starting point?
So, no change in 1st 100 mile + no change in 2nd 100 mile+ change in 3rd 100 miles
So, the probability that the first change of tire occurred 300 miles from his starting point = 0.95 * 0.95 * 0.05 =0.0451
Hence the probability that the first change of tire occurred 300 miles from his starting point is 0.0451
b) What is the probability that his second change of tire occurred 500 miles from his starting point?
So, no change in 1st 400 miles + change in last 100 miles
So,the probability that his second change of tire occurred 500 miles from his starting point = [tex]^4C_1 \times 0.05 \times (0.95)^3 \times 0.05[/tex]
= [tex]0.0514[/tex]
Hence the probability that his second change of tire occurred 500 miles from his starting point 0.0514
c) What is the probability that he completed the trip without having to change tires?"
No change after 800 miles
Probability that he completed the trip without having to change tires :
= [tex](0.95)^8[/tex]
= [tex]0.6634[/tex]
Hence the probability that he completed the trip without having to change tires is 0.6634
