You have an important test tomorrow morning and want to be sure to wake up at 6:00 AM to study.Without an alarm to wake you up, you know you have no chance.You have an alarm clock that works 80% of the time.To be on the safe side, you decide to set both your alarm clock and your roommate's alarm clock-also 80% reliable.How likely is it you'll be awakened at the proper time? (Assume statistical independence.)
A).04
B).64
C).36
D).96
E).16

Question

Quizplus · Accepted Answer

The probability of not waking up with one alarm clock is 20% (100% - 80%). Since the alarms are independent, the probability of both failing is 20% * 20% = 4% (0.2 * 0.2 = 0.04). Therefore, the probability of waking up (at least one alarm working) is 100% - 4% = 96%.

You Have an Important Test Tomorrow Morning and Want to Be