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  Shota built a time travel machine, but he can't control the duration of his trip. Each time he uses the machine he has a 0.8 probability of staying in the alternative time for more than an hour. During the first year of testing, Shota uses his machine 20 times.

Assuming that each trip is equally likely to last for more than an hour, what is the probability that at least one trip will last less than an hour?
Round your answer to the nearest hundredth.

    P(at least one<1 hour)=_____

 Nov 27, 2018
 #1
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\(P[\text{at least one trip will last less than one hour}] = \\ 1- P[\text{all trips last 1 hr or more}] = \\ 1 - (0.8)^{20} = 0.9999999999999895 \\ \text{so pretty likely}\)

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 Nov 27, 2018

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