Question

Assume A, B, C, and D function independently. If the probabilities that A, B, C, and D fail are 0.10, 0.05, 0.10 and 0.20, respectively, what is the probability that the system functions?

Answer 1

Answer:

The probability that the system function is 0.6156

Step-by-step explanation:

We can calculate the chances of two or more independent events by multiplying the chances.

Since the chances of fail are given, to get the chance of pass, we subtract from 1.

Probability that it works = 1 - prob that it fails

For A (probability of fail = 0.10)

Probability that it works = 1 - 0.10 = 0.9

For B (probability of fail = 0.05)

Probability that it works = 1 - 0.05 = 0.95

For C (probability of fail = 0.10)

Probability that it works = 1 - 0.10 = 0.9

For D (probability of fail = 0.20)

Probability that it works = 1 - 0.20 = 0.8

Therefore, the probability that the system function is:

$0.9 * 0.95 * 0.9 * 0.8 = 0.6156$

Approximately, the probability can be written as 0.6 to one decimal place.