If a certain kind of tire has a life exceeding 40,000 miles with probability 0.90, what is the probability that a set of these tires on a car will last longer than 40,000 miles?
Answers
Answer:
Step-by-step explanation:
Probability of a tyre having a life more than 40,000 miles = 0.90
For a set of tyres ( 4 tyres ), to have a life more than 40,000 miles, each of them should independently have a life more than 40,000 miles.
Hence, required probability =
0.9 x 0.9 x 0.9 x 0.9 = 0.6561
The probability that the set will last longer than 40,000 miles is 0.6561
GIVEN: A certain kind of tire has a life exceeding 40,000 miles with a probability of 0.90.
TO FIND: Probability that a set of these tires on a car will last longer than 40,000 miles
SOLUTION:
As we are given in the question,
A certain kind of tire has a life exceeding 40,000 miles with a probability of 0.90
Therefore,
Probability of a single tire having a life of more than 40,000 miles = 0.90
Therefore,
For a set of 4 tires, to have a life of more than 40,000 miles, each of them should independently have a life of more than 40,000 miles.
Therefore,
Probability of set to have life more than 40,000 miles = P(E)⁴
Hence, the required probability
=P(E)*P(E)*P(E)*P(E)
= 0.9 x 0.9 x 0.9 x 0.9
= 0.6561
Therefore,
The required probability is 0.6561.
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