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

B

Explanation

Let `A_(i)`= Event of getting a number I on first die `B_(i)`= Event of getting a number more than I or second die.
The required probability
`=P(A_(1) cap B_(1))+P(A_(2) cap B_(2))+P(A_(3) cap B_(3)) +P(A_(4) cap B_(4))+P(A_(S) capB_(S))`
`=underset(i=1)overset(5)sum P(A_(i) cap B)==underset(i=1)overset(5)sum P(A_(i))P(B_(i))` [`therefore A_(i), B_(i)` are independent events)
`=(1)/(6)[P(B_(i))+P(B_(2))+......+P(B_(i))]`
`=(1)/(6)[(5)/(6)+(4)/(6)+(3)/(6)+(2)/(6)+(1)/(6)]=(5)/(12)`