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In a binomial distribution B(n , p=1/4) ...

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)`

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)`

Text Solution

Verified by Experts

The correct Answer is:
A
`1-q^(n) ge (9)/(10)`
`implies ((3)/(4))^(n) le (1)/(10)`
`implies n ge -"log"_(3//4)10`
`implies n ge (1)/("log"_(10)4-"log"_(10)3)`
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