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In: Statistics and Probability

(b) The battery in Ali’s phone runs out at random moments. Over a long period, he...

(b) The battery in Ali’s phone runs out at random moments. Over a long period, he found that the battery runs out, on average 4 times in a 30-day period.

(i) Find the probability that the battery runs out fewer than 3 times in a 25-day period.

(ii) Find the probability that the battery runs out more than 50 times in a year (365 days).

(iii) Independently of his phone battery, Ali’s computer battery also runs out at random moments. On average, it runs out twice in a 15-day period. Find the probability that the total number of times that his phone battery and his computer battery run out in a 10-day period is at least 4.

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