You have a very important job interview at 8:00 AM tomorrow. Unfortunately, you do not have a reliable alarm clock. In fact,the three alarm clocks you have only ring some of the time. The first clock only rings 20% of the time, the second clock only rings 30% of the time, and the third clock only rings 50% of the time. If you set each of them to ring at 6:30 AM, what is the probability that you will be alerted to get up at the correct time?
a 0%
b 3%
c 100%
d cannot determine from the given information
e none of the above
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This is the probability that AT LEAST ONE of the three alarm clocks will
ring.
P(at least one rings) = 1 - P(all three fail to ring) =
1 - P(1st fails to ring AND 2nd fails to ring AND 3rd fails to ring).
Since the events of them failing to ring are independent, "AND" means
we can multiply their probabilities, and the desired probability is
given by:
1 - P(1st fails to ring)×P(2nd fails to ring)×P(3rd fails to ring).
Since the first one rings 20% of the time, the probability that it
fails to ring is 80% or .8
Since the second one rings 30% of the time, the probability that it
fails to ring is 70% or .7
Since the third one rings 50% of the time, the probability that it
fails to ring is also 50% or .5
Therefore
P(at least one rings) = 1 - P(none ring) =
1 - P(1st fails to ring)×P(2nd fails to ring)×P(3rd fails to ring) =
1 - (.8)(.7)(.5) = 1 - .28 = .72 or 72%
Since 72% is not listed the correct choice is "(e) none of the above".
Edwin