a kind of tire has a 80% probability of exploding after 20000 miles. What is the probability that a set of 4 tires will last longer that 20000 miles without any of tham exploding?

Probability of one tire NOT exploding = 1-80%=0.2

Probability of ALL FOUR tires NOT exploding = 0.2^4 = 0.0016

tell me answe

To determine the probability that all four tires in a set will last longer than 20000 miles without any of them exploding, we need to multiply the individual probabilities of each tire lasting longer than 20000 miles.

Given that each tire has an 80% probability of exploding after 20000 miles, the probability of a single tire not exploding after 20000 miles is 1 - 0.8 = 0.2 (since 100% - 80% = 20%).

Assuming the tires operate independently (the failure of one tire does not affect the others), we can multiply the probabilities of individual events to find the probability of all four tires not exploding.

Therefore, the probability that all four tires in a set will last longer than 20000 miles without any of them exploding is:
0.2 * 0.2 * 0.2 * 0.2 = 0.0016 or 0.16%.