Alarm Clock Life Hack Each of us must sometimes wake up early ...

Question

Alarm Clock Life Hack Each of us must sometimes wake up early for something really important, such as a final exam, job interview, or an early flight. (Professional golfer Jim Furyk was disqualified from a tournament when his cellphone lost power and he overslept.) Assume that a battery-powered alarm clock has a 0.005 probability of failure, a smartphone alarm clock has a 0.052 probability of failure, and an electric alarm clock has a 0.001 probability of failure.

b. If you use a battery-powered alarm clock and a smartphone alarm clock, what is the probability that they both fail? What is the probability that both of them do not fail?

b. If you use a battery-powered alarm clock and a smartphone alarm clock, what is the probability that they both fail? What is the probability that both of them do not fail?

Accepted Answer

All right. Hello, everyone. So this question says, in a remote work setup, you rely on two different internet connections to ensure uninterrupted work. A primary fiber optic connection with a 0.003 probability of failure, and a backup satellite connection with a 0.020 probability of failure. What is the probability that both internet connections fail? What is the probability that both do not fail? All right, so in this question, we're given the probability of failure for each connection separately. Starting off with our, let's see here, our primary fiber optic connection. The probability of the fiber optic failure, or PFF as I'm writing here, is equal to 0.003. And the probability of the satellite failure. Is equal to 0.020. So if you want to find the probability. Of both Internet connections failing. What you do is multiply the individual probabilities together. Which means that the probability of both is equal to 0.003, multiplied by 0.020. Which gives you 0 point. 00006 And so to find the probability that both do not fail, you would repeat a similar calculation. The difference, however, is that the probability of each network or each connection not failing is one subtracted by the probability of failure. So, for example, the probability that the fiber optic connection works is equal to 1, subtracted by 0.003. Which gives you 0.997. And so the probability of the satellite network working. Is one subtracted by 0.020. Which gives you 0.980. And so to find the probability. Of both working. That would be 0.997. Multiplied by 0.980. Which gives you 0.97706. And so from that, we have our final answer. So the probability of both failing is 0.00006. And the probability of both not failing is 0.97706. And there you have it. So with that being said, thank you so very much for watching, and I hope you found this helpful.

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Key Concepts

Probability of Independent Events

Complementary Probability

Joint Probability

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