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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)`

Text Solution

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`0,1,2,3,4,..... , n`
`P= 1- `all fail
`S(P) = 1/4`
`S(F) = 1 - S(P)`
`= 1-1/4`
`=3/4`
`P= 1- (3/4)^n >= 9/10`
`-9/10 >= (3/4)^n`
...
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