Let's consider the time as a discrete variable with an increment of 1 minute. You arrive at a bus stop at 10 AM, knowing that the bus will arrive at some time uniformly distributed between 10 and 10:30.

(a) What is the probability that you will have to wait longer than 10 minutes?

(b) If, at 10:10, the bus has not yet arrived, what is the probability that you will have to wait at least an additional 10 minutes?

Question

Derrick Boyle

Mathematics

21 February, 11:08

Let's consider the time as a discrete variable with an increment of 1 minute. You arrive at a bus stop at 10 AM, knowing that the bus will arrive at some time uniformly distributed between 10 and 10:30.

(a) What is the probability that you will have to wait longer than 10 minutes?

(b) If, at 10:10, the bus has not yet arrived, what is the probability that you will have to wait at least an additional 10 minutes?

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Answers (1)

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Ollie · Answer 1

a) 2/3

b) 1/3

Step-by-step explanation:

Let X be the random event that measures the time you will have to wait.

Since time is uniformly distributed between 10 and 10:30 in intervals of 1 minute

P (n < X ≤ n+1) = 1/30 for every minute n=0,1, ... 29.

a)

P (X > 10) = 1 - P (X ≤ 10) = 1 - 10/30 = 2/3

b)

P (10 < X ≤ 20) = (20-10) / 30 = 1/3