A die is tossed thrice. If event of getting an even number is a success. Then the probability of getting at least two successes is

Options

A. `(7)/(8)`
B. `(1)/(4)`
C. `(2)/(3)`
D. `(1)/(2)`

Answer

D

Explanation

(d) Let `E={2,4,6}`
Tehn, n(E )=3 and n(S)=6
Probability of success `=P(E )=(n(E ))/(n(S))=(1)/(2)`
Probability of failure `=1-(1)/(2)=(1)/(2)`
`:.` Probability of atleast two successes
`=P(X=2)+P(X=3)`
`=""^(3)C_(2)((1)/(2))^(2)((1)/(2))^(1)+""^(3)C_(3)((1)/(2))^(3)((1)/(2))^(3)((1)/(2))^(0)=(3)/(8)+(1)/(8)=(1)/(2)`