Two numbers are selected at random from integers 1 through 9. If the sum is even, find the probability that both the numbers are odd.

Options

A. `(1)/(6)`
B. `(2)/(3)`
C. `(4)/(9)`
D. `(5)/(8)`

Answer

D

Explanation

Out of given 9 numbers 4 are even and 5 odd.
Let A = event of choosing odd number and B be the event of getting the sum even .
`n(B)=(.^(4)C_(2) +.^(5)C_(2)) =16 " and " n(A nn B) =.^(5)C_( 2) =10`
`:. P(A //B) =(n(A nn B))/(n(B)) =(10)/(6) =(5)/(8)`