Find the indicated probability. Round to four decimal places.
-A machine has 7 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.
A)0.9667
B)0.0333
C)0.8853
D)0.1147

Question

Find the indicated probability. Round to four decimal places.
-A machine has 7 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. 
A)0.9667
B)0.0333
C)0.8853
D)0.1147

Quizplus · Accepted Answer

The probability that the machine will be working is the complement of the probability that more than three components fail. To find this, we calculate the probability of 0, 1, 2, or 3 failures and subtract from 1. Using the binomial probability formula, we sum the probabilities of exactly 0, 1, 2, and 3 failures happening, which gives us the probability of the machine working. The calculation shows that the probability of the machine working is approximately 0.9667.

Find the Indicated Probability