Three cards with replacement are drawn from a deck of 52 well shuffled cards, X denote the random variable of number of face cards drawn, then `P(X =1) + P(X = 2)` equals:

Options

A. `1070/(13^3)`
B. `(90)/(169)`
C. `30/(169)`
D. `1270/(13^3)`

Answer

B

Explanation

P(Face card) `= 12/52 = 3/13`
`P(X = 1) = .^(3)C_(1) (3/13)^(1) (10/13)^2`
`P(X = 2) = .^(3)C_(2) (3/13)^2 (10/13)^(-1)`
`P(X = 1) + P(X = 2) = 90/169`.