Question

A machine is known to never last more than four months. During its first month of operation, it fails 10% of the time. If the machine completes its first month, then it fails during its second month 20% of the time. If the machine completes its second month of operation, then it will fail during its third month 50% of the time.

a) 1st month failure = 10%, 2nd month failure = 20%, 3rd month failure = 50%
b) 1st month failure = 90%, 2nd month failure = 80%, 3rd month failure = 50%
c) 1st month failure = 10%, 2nd month failure = 2%, 3rd month failure = 50%
d) 1st month failure = 90%, 2nd month failure = 18%, 3rd month failure = 50%

Answer 1

The correct answer is b. 1st month failure = 90%, 2nd month failure = 80%, 3rd month failure = 50%.

Step-by-step explanation:

The correct answer is b. 1st month failure = 90%, 2nd month failure = 80%, 3rd month failure = 50%.

Based on the information given in the question, the failure rates for each month are as follows:

• 1st month failure = 10%
• 2nd month failure = 20% (if the machine completes its first month)
• 3rd month failure = 50% (if the machine completes its second month)

Therefore, the failure rates for the three months are 10%, 20%, and 50% respectively. To determine the success rates for each month, subtract the failure rates from 100%:

• 1st month success = 100% - 10% = 90%
• 2nd month success = 100% - 20% = 80%
• 3rd month success = 100% - 50% = 50%

So, the correct answer is (b) 1st month failure = 90%, 2nd month failure = 80%, 3rd month failure = 50%.