5.2-06 – Introductory Statistics – Sheldon M. Ross

Question:

Two people are to meet in the park. Each person is equally likely to arrive, independent of the other, at 2:00, 2:30, or 3:00 pm. Let X equal the time that the first person to arrive has to wait, where X is taken to equal 0 if both people arrive at the same time.

(a)            What are the possible values of X?

(b)           What are the probabilities that X assumes each of these values?

Solution:

Person 1 arrival time	Person 2 arrival time	The time that the first person to arrive has to wait
2:00	2:00	0 mins
	2:30	30 mins
	3:00	60 mins
2:30	2:00	30 mins
	2:30	0 mins
	3:00	60 mins
3:00	2:00	60 mins
	2:30	30 mins
	3:00	0 mins

Answer (a):

The possible values that X can take are:

·        0 mins

·        30 mins

·        60 mins

Answer (b):

Let X = the time that the first person to arrive has to wait

Probability distribution of X is as below

X	Frequency	P(X)
0 mins	3	3/9
30 mins	4	4/9
60 mins	2	2/9
Total	9	9/9