In a binomial distribution `B(n , p=1/4)` , if the probability of at least one success is greater than or equal to `9/(10)` , then n is greater than (1) `1/((log)_(10)^4-(log)_(10)^3)`
(2) `1/((log)_(10)^4+(log)_(10)^3)`
(3) `9/((log)_(10)^4-(log)_(10)^3)`
(4) `4/((log)_(10)^4-(log)_(10)^3)`

Options

A. `(1)/(log_(10)4-log_(10)3)`
B. `(1)/(log_(10)4+log_(10)3)`
C. `(9)/(log_(10)4-log_(10)3)`
D. `(4)/(log_(10)4-log_(10)3)`

Answer

A

Explanation

According to the question
`1-q^(n)ge9/10`
`implies((3)/(4))^(n)ge1/10`
`impliesnge-log_(3/4)10`
`=nge(1)/(log_(10)4-log_(10)3)`