Question

It has been found that 6% of all automobiles on the road have defective brakes. If 5 automobiles are stopped and checked by the police, find the probability that at LEAST one will have defective brakes.

Answer 1

To find the probability that at least one automobile will have defective brakes out of 5 cars, we can use the complement rule. The probability that at least one car will have defective brakes is 0.2649, or approximately 26.49%.

Step-by-step explanation:

To find the probability that at least one automobile will have defective brakes out of 5 cars, we can use the complement rule. The complement rule states that the probability of an event not occurring is equal to 1 minus the probability of the event occurring.

The probability that none of the 5 cars will have defective brakes is the complement of the probability that at least one car will have defective brakes.

Using the complement rule, the probability that at least one car will have defective brakes is equal to 1 minus the probability that none of the cars will have defective brakes.

P(None of the cars have defective brakes) = (1 - P(One car has defective brakes))^5

P(None of the cars have defective brakes) = (1 - 0.06)^5

P(None of the cars have defective brakes) = 0.945

P(None of the cars have defective brakes) = 0.7351

The probability that at least one car will have defective brakes is 1 - 0.7351 = 0.2649, or approximately 26.49%.