Answer:
Pr(X=1) = 1/36
Pr(X=2) = 3/36
Pr(X=3) = 5/36
Pr(X=4) = 7/36
Pr(X=5) = 9/36
Pr(X=6) = 11/36
Pr(X is divisible by 4) = 7/36
Step-by-step explanation:
Two fair die are thrown and X = maximum of the two die.
Pr(X=1) means 1 is the maximum number of the two numbers showing on the dice. This can only happen when both dice are showing 1. So,
Pr(X=1) = (1,1)
= (1/6)*(1/6)
Pr(X=1) = 1/36
Pr(X=2) = (1,2) + (2,1) + (2,2)
= (1/6)*(1/6) + (1/6)*(1/6) + (1/6)*(1/6)
Pr(X=2) = 3/36
Pr(X=3) = (1,3) + (2,3) + (3,1) + (3,2) + (3,3)
= (1/6)*(1/6) + (1/6)*(1/6) + (1/6)*(1/6) + (1/6)*(1/6) + (1/6)*(1/6)
Pr(X=3) = 5/36
Pr(X=4) = (1,4) + (2,4) + (3,4) + (4,1) + (4,2) + (4,3) + (4,4)
= (1/6)*(1/6)+(1/6)*(1/6)+(1/6)*(1/6)+(1/6)*(1/6)+(1/6)*(1/6)+(1/6)*(1/6)+(1/6)*(1/6)
Pr(X=4) = 7/36
Pr(X=5) = (1,5) + (2,5) + (3,5) + (4,5) + (5,1) + (5,2) + (5,3) + (5,4) + (5,5)
= 9 *(1/6)*(1/6)
Pr(X=5) = 9/36
Pr(X=6) = (1,6) + (2,6) + (3,6) + (4,6) + (5,6) + (6,1) + (6,2) + (6,3) + (6,4) + (6,5) + (6,6)
= 11 * (1/6)*(1/6)
Pr(X=6) = 11/36
X is divisible by 4 only when X=4. Other values of X are not divisible by 4. So,
Pr(X is divisible by 4) = Pr(X=4)
Pr(X is divisible by 4) = 7/36
