Question

Break downs occur on a 20-years-old car with rate λ= 0.5 breakdowns/week. The owner of the car is planning to have a trip on his car for 2 weeks. What is the probability that there will be no breakdown on his car in the trip?

Answer 1

Answer: There is probability of 0.367 that there will be no breakdown on his car in the trip.

Step-by-step explanation:

Since we have given that

Mean (λ) = 0.5 breakdown per week

Number of weeks the owner of the car is planning to have a trip on his car for = 2 weeks

So, mean for 2 weeks would be

$0.5\times 2=1.0$

We need to find the probability that there will be no breakdown on his car in the trip.

Probability that there will be no breakdown on his car in the trip is given by

P(X=0) is given by

$\dfrac{e^{-\lambda}\lambda^k}{k!}\\\\=\dfrac{e^{-1}1^0}{0!}\\\\=0.367$

Hence, there is probability of 0.367 that there will be no breakdown on his car in the trip.