Question

The probability that a particular electrical component operates successfully is . an electrical system consists of three such components that operate independently. the system will function successfully if at least one of the three components operates successfully.

a. 1/64
b. 27/64
c. 37/64
d. 3/4
e. 63/64

Answer 1

To find the probability that at least one of the three components operates successfully, we can use the complement rule. The probability of at least one component operating successfully is 1.

Step-by-step explanation:

To find the probability that at least one of the three components operates successfully, we can use the complement rule. The complement of at least one component operating successfully is none of the components operating successfully.

The probability of a component operating successfully is 1, and the probability of a component failing is 1 - 1 = 0. Since the components operate independently, we can find the probability that none of the components operate successfully by multiplying the probabilities of each component failing together: 0 * 0 * 0 = 0.

Finally, we can use the complement rule to find the probability of at least one component operating successfully: 1 - 0 = 1. Therefore, the probability is 1.

Answer 2

To find the probability that at least one of the three electrical components operates successfully, use the complementary probability. Given that the probability of a component operating successfully is p, the probability that at least one of the three components operates successfully is 1 - (1 - p)^3.

Step-by-step explanation:

To find the probability that at least one of the three electrical components operates successfully, we will use the complementary probability. The complementary probability is the probability that the event does not occur. In this case, the event is that none of the three components operate successfully.

The probability of a component not operating successfully is 1 - p, where p is the probability of a component operating successfully.

Since the components operate independently, the probability of all three components not operating successfully is (1 - p)^3.

Therefore, the probability that at least one of the three components operates successfully is 1 - (1 - p)^3.

Given that the probability of a component operating successfully is p, the probability that at least one of the three components operates successfully is 1 - (1 - p)^3.