Question

You are the proud owner of a brand-new Audi Quattro. Unbeknownst to you, the car has a manufacturing defect that causes it to have a ₅₀₀₀¹ chance of exploding each time you turn it on.

1. What is the probability that it will explode the first time you turn it on?
2. What is the probability that it will explode the 100^th time you turn it on?
3. What is the probability that is will explode at any point in the first 5000 times that you turn it on?

Answer 1

I think there is atyping mistake the chance must be 5000 : 1

P(explode) = 1/5000

P(doesn't explode) = 1 - P(explode)

= 1 - 1/5000

P(doesn't explode) = 4999/5000

(1) P(explode the first time you turn it on) = P(explode) = 1/5000

(2) P(explode the 100th time you turn it on) = P(doesn't explode in first 99 times)*P(explode)

= ((4999/5000)99)*(1/5000)

P(explode the 100th time you turn it on) = 0.00019

(3) P(explode at any point in the first 5000 times) = 1 - P(doesn't explode in first 5000 times)

= 1 - (4999/5000)5000

P(explode at any point in the first 5000 times) = 0.632

(please upvote the solution if u find it satisfactory)