A die is rolled thrice . If the event of getting an even number is a success , then the probability of getting atleast two sucessess is

Options

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

Answer

D

Explanation

Let X denote the number of successes in 3 trials. Then, X is a binomial variate with `n=3,p=(3)/(6)=(1)/(2)` such that
`P(X=r)=.^3C_(r)((1)/(2))^3,r=0,1,2,3`
`therefore` Required Probability `=P(Xge 2)=P(X=2)+P(X=3)`
`=.^3C_2((1)/(2))^3+.^3C_(3)((1)/(2))^3=(1)/(2)`