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A guard works between 5 p.m. and 12 midnight; he sleeps an average of 1 hour...

A guard works between 5 p.m. and 12 midnight; he sleeps an average of 1 hour before 9 p.m. and 1.5 hours between 9 and 12. An inspector finds him asleep, what is the probability that this happens before 9 p.m.?

Math   Statistics-And-Probability   
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Answer #1

The guard works for a total of 7 hours.

P(Time between 5 and 9) = 4/7

P(Time between 9 and 12) = 3/7

P(sleep between 5 and 9 PM) = 1/4

P(Sleep between 9 and 12) = 1.5/3 = 1/2

We need to find the probability:

P(Time between 5 and 9/ Sleeping)

= P(Sleeping between 5 and 9) / P(Sleeping)

{Using Bayes theorem}

Hence the required probability is 40%.

Please do upvote if you are satisfied! Let me know in the comments if anything is not clear. I will reply ASAP!

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