Question

Random variable X counts the number of times doubles is rolled (i.e. the same number comes up on both dice) when two ordinary (6-sided) fair dice are rolled seven times. How many possible values does Xhave?

A. 6

b. 7

C. 8

D. 30

E. 36

Answer 1

Let X1 be the number occurred when first die is thrown, X1 can take value 1,2,3,4,5 or 6

Let X2 be the number occurred when second die is thrown, X2 can take value 1,2,3,4,5 or 6

X = number of times doubles that is number of times ( X1=X2) out of 7 throws of 2 die

X can take value 0 ( 0 success out of 7 throws)

X can take value 1 ( 1 success out of 7 throws )

And so on till X can take value 7 ( 7 success out of 7 throws )

So, X can take 8 values ( 0,1,2,3,4,5,6 or 7 )

So option C - 8