If you bought a new set of four tires from manufacturer who just announced recall because 10 percent those are defective What is the probability that at least on yours defective?

The probability of at least one of your tires being defective can be calculated using the complement rule of probability, which states that the probability of an event occurring is equal to 1 minus the probability of it not occurring.

Let's define the following events:

A: Your first tire is defective.

B: Your second tire is defective.

C: Your third tire is defective.

D: Your fourth tire is defective.

Then, the probability that none of your tires are defective is:

P(none defective) = P(A' and B' and C' and D')

Since the tires are independent events, we can multiply the probabilities of each event not being defective:

P(none defective) = (0.9)^4 = 0.6561

Therefore, the probability that at least one of your tires is defective is:

P(at least one defective) = 1 - P(none defective) = 1 - 0.6561 = 0.3439

So, there is a 34.39% chance that at least one of your new tires is defective.