Question

A six sided die is marked ‘2’ on one face, ‘3’ on two of its faces, and ‘4’ on remaining three faces. The die is thrown twice. If X denotes the total score in two throws, find the values of the random variable and number of points in its inverse images.

Answer 1

Six sided die marked ‘2’ on one face, ‘3’ on two faces and ‘4’ on three faces.

When it is thrown twice, we get 36 sample points. 

‘X’ denotes sum of the face numbers and the possible values of ‘X’ are 4, 5, 6, 7 and 8 

For X = 4, the sample point is (2, 2) 

For X = 5, the sample points are (2, 3), (3, 2) 

For X = 6, the sample points are (3, 3), (2, 4), (4, 2) 

For X = 7, the sample points are (3, 4), (4, 3) 

For X = 8, the sample point is (4, 4)

Values of X	4	5	6	7	8	Total
Number of elements in inverse images	1	2	3	2	1	9