You have worked for the Department of Administrative Affairs (DAA) for 27 years, and you still have little or no idea exactly what your job entails. To make your life a little more interesting, you have decided on the following course of action. Every Friday afternoon, you will use your desktop computer to generate a random digit from 0 to 9 (inclusive). If the digit is a eight or greater, you will immediately quit your job, never to return. Otherwise, you will return to work the following Monday. What is the probability that you will still be employed by the DAA after each of the next three weeks ?
A)0.992
B) 0.64
C) 0.512
D) 1
E) 0.8

Question

You have worked for the Department of Administrative Affairs (DAA) for 27 years, and you still have little or no idea exactly what your job entails. To make your life a little more interesting, you have decided on the following course of action. Every Friday afternoon, you will use your desktop computer to generate a random digit from 0 to 9 (inclusive). If the digit is a eight or greater, you will immediately quit your job, never to return. Otherwise, you will return to work the following Monday. What is the probability that you will still be employed by the DAA after each of the next three weeks  ?
A)0.992
B) 0.64
C) 0.512
D) 1
E) 0.8

Quizplus · Accepted Answer

The probability of not quitting each week is 8/10 or 0.8, since there are 8 digits (0-7) that result in staying employed and 2 digits (8-9) that result in quitting. To find the probability of staying employed for three consecutive weeks, multiply the probability of staying employed each week by itself three times: $0.8 \times 0.8 \times 0.8 = 0.512$. However, the correct calculation should be $0.8^3 = 0.512$, indicating a mistake in the final selection of the correct answer. The correct probability calculation for staying employed after three weeks is indeed $0.8^3$, but the correct answer choice should reflect the calculation outcome, which is 0.512, not 0.8. Therefore, the intended correct answer choice and explanation seem to have been mismatched in my response. The correct answer, based on the calculation provided, should be C) 0.512, not E) 0.8.

You Have Worked for the Department of Administrative Affairs (DAA)