Bob sets two alarm clocks (battery-powered) to be sure he arises for his Monday 8:00 a.m. accounting exam. There is a 75 percent chance that either clock will wake Bob.
(a) What is the probability that Bob will oversleep? (Round your answer to 4 decimal places.)
(b) If Bob had three clocks, would he have at least a 99 percent chance of waking up?

Question

19-12-2022
Mathematics

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Bob sets two alarm clocks (battery-powered) to be sure he arises for his Monday 8:00 a.m. accounting exam. There is a 75 percent chance that either clock will wake Bob.
(a) What is the probability that Bob will oversleep? (Round your answer to 4 decimal places.)
(b) If Bob had three clocks, would he have at least a 99 percent chance of waking up?

Answer :

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debjitbhowal4568 debjitbhowal4568 · Answer 1 · 2022-12-23T23:18:22-05:00

The probability that Bob will oversleep is 6.25%.

The study of probability examines the likelihood that a certain event will really occur or not. Depending on the nature of the occurrences, a probability problem will require a certain procedure. The basis for the kind of events has three components: Independent, Dependent, and Mutually Exclusive Events.

There is a 75% chance that either clock will wake Bob. Thus, the probability that the clock will not wake Bob up is equal to

P (N) = 1-75% = 1- 0.75

P (N) = 0.25

Since the two clocks are considered to be an independent event, then the probability that Bob will oversleep is

P(oversleep) = P (N)*P (N) = 0.25*0.25 = 0.0625

P(oversleep) = 6.25%

Thus, the probability that Bob will oversleep is 6.25%.

If bob ad three clocks then the probability that Bob will oversleep is

P(oversleep) = P (N)*P (N)*P (N)= 0.25*0.25 *0.25 = 0.015625

P(oversleep) = 1.56%

Thus, the probability that Bob will oversleep even after three clocks is 1.56%.

The chances of bob waking up after having three clocks is 98.44%

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