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 a tire cannot have one tire defective and two tires defective at the same time, I considered the events to be disjoint. I used the addition rule:

P(1 tire is defective) + P(2 tires are defective) + P(3 tires are defective) + P(4 tires are defective)

To find the probability of two tires being defective, I multiplied .02*.02. To find the probability that three tires being defective, I multiplied .02*.02*.02. And, so on for the four tires.. This is because the problem stated that they are independent.

I ended up with the wrong answer. Can someone please help me? ]]>