Question

Consider the experiment where a pair of fair dice is thrown. Let X denote the random variable whose value is determined by multiplying the number of spots showing on the one die by the number of spots showing on the other. The range of values that X can assume are the positive integers {1,2,3,4,5,6,8,9,10,12,15,16,18,20,24,25,30,36}. Please give the corresponding probabilities for the values of X given below.

Answer 1

Explanation:

Let the Variable "a" and "b" denoted the the number on the dice.

As per question let X be random variable.

Step 1:

X=1, then (a,b) = (1,1)

so P(X=1) = 1/36

Step 2:

X=2, then (a,b) = (2,1) (1,2)

so P(X=2) = 2/36

Step 3:

X=3, then (a,b) = (3,1) (1,3)

so P(X=3) = 2/36

Step 4:

X=4, then (a,b) = (4,1) (1,4)

so P(X=4) = 3/36

Step 5:

X=5, then (a,b) = (5,1) (1,5)

so P(X=5) = 2/36

When X is divisible by 4 and variable "a" and "b" can be even number and one of them can be the multiple of 4 and other can be odd

P(X= m(4)) = (3 * 3) + (1 * 3) / 36 = 1/3