Question

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?

Answer 1

Answer:

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