Question: You recently bought a new set of four tires from a manufacturer who just announced a recall because 2% of that particular brand of tires are defective. What is the probability that at least one of your tires is defective? You may assume that the tires are defective independently of one another.


Since the probabilities of 1 tire and 2 tires being defective at the same time was disjoint, I proceeded by setting up a sum as per the addition rule. In other words, you can't have 2 and 3 tires defective. So, they are disjoint.

So, it was the P(1 tire being defective) + P(2 tires being defective) + P(3 tires being defective) + P(4 tires being defective)
To find P(2 tires being defective), I multiplied .02*.02 and so on because the question states they're independent.
So, I did (.02) + (.02)^2 + (.02)^3 + (.02)^4.

I keep getting the answer wrong. Can someone help? I am a college student taking stats with no previous stats experience whatsoever, and I am trying my level best to catch up.