Two dice are rolled one after the other.The probability that the number on the first dice is smaller than that of the number on second dice is-

Options

A. `1//2`
B. `7//18`
C. `3//4`
D. `5//12`

Answer

D

Explanation

Consider two events as follows:
`A_(i):` getting number inon first die
`B_(i),` getting a number more than in on second die The required proability is
`P(A_(1)nnB_(1))+P(A_(2)nnB_(2))+P(A_(3)nnB_(3))+P(A_(4)nnB_(4))+P(A_(5)nnB_(5))=underset(i=1)overset(5)sumP(A_(i)nnB_(i))=underset(i=1)overset(5)sumP(A_(i)P(B_(i))`
`" "[becauseA_(i),B_(i)"are independent"]`
`=1/6[P(B_(1))+P(B_(2))+...+P(B_(5))]`
`=1/6((5)/(6)+(4)/(6)+(3)/(6)+(2)/(6)+(1)/(6))=5/12`