A teacher surveyed her students about the amount of time the students
1 answer:
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Answer:
1/4
Step-by-step explanation:
Let X be the time of arrival measured from the beginning of the 30-minute period.
Since the number of arrivals is Poisson, the time of the arrival is equally likely in any subinterval of time of a given size in the 30 minutes, and thus X has a uniform distribution in (0,30) and P(X > 25) =
where a = 30 and b = 25
Solving, we obtain P(X > 25) = 1/6
similarly, P(X>10) = 2/3 by substituting b for 10
Hence, for conditional probability we have
P(X>25 | X>10) = P(X>25) / P(X>10) = (1/6) / (2/3) = 1/4