Question

A machine has 9 identical components which function independently. the probability that a component will fail is 0.2. the machine will stop working if more than three components fail. find the probability that the machine will be working.

1. 0.914
2. .914%
3. 91.4
4. 9.14

Answer 1

To find the probability that the machine will be working, we use the binomial probability formula with n = 9 and p = 0.2, and calculate P(X ≤ 3). The answer is 0.914.

Step-by-step explanation:

To find the probability that the machine will be working, we need to find the probability that three or fewer components fail. Since each component functions independently, we can use the binomial probability formula.

The formula for the probability that exactly k successes occur in n independent trials, each with probability of success p, is:

P(X=k) = C(n, k) * p^k * (1-p)^(n-k)

In this case, n = 9, p = 0.2, and we want to find P(X ≤ 3). So we need to calculate:

P(X ≤ 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)

Using this formula, we can find that the probability that the machine will be working is 0.914, which is answer option 1.