Question

Two dice are rolled. Let X be the maximum number obtained. (Thus, if 1 and 2 are rolled, X = 2; if 5 and 5 are rolled, X = 5.) Assume that all 36 elements of the sample space are equally likely. Find the probability function for X. That is, find P(X = x), for x = 1, 2, 3, 4, 5, 6.

Answer 1

x	P(X=x)
1	1//36
2	3//36
3	5//36
4	7//36
5	9//36
6	11//36

following number pair on dice 1 and dice 2 are shown and corresponding X is denoted according to question. each number pair has probability 1/36

number pair	X	number pair	X	number pair	X
(1,1)	1	(1,2)	2	(1,3)	3
(2,1)	2	(2,2)	2	(2,3)	3
(3,1)	3	(3,2)	3	(3,3)	3
(4,1)	4	(4,2)	4	(4,3)	4
(5,1)	5	(5,2)	5	(5,3)	5
(6,1)	6	(6,2)	6	(6,3)	6
number pair	X	number pair	X	number pair	X
(1,4)	4	(1,5)	5	(1,6)	6
(2,4)	4	(2,5)	5	(2,6)	6
(3,4)	4	(3,5)	5	(3,6)	6
(4,4)	4	(4,5)	5	(4,6)	6
(5,4)	5	(5,5)	5	(5,6)	6
(6,4)	6	(6,5)	6	(6,6)	6