An unbiased normal coin is tossed n times. Let
`E_(1):` event that both heads and tails are present in n tosses.
`E_(2):` event that the coin shows up heads at most once.
The value of n for which `E_(1) and E_(2)` are independent is ______.

Explanation

`P(E_(1))=1-["P(all heads)+P(all tails")]`
`=1-[(1)/(2^(n))+(1)/(2^(n))]=1-(1)/(2^(n-1))`
`P(E_(2))=P("no head)+P(exactly one head")`
`=(1)/(2^(n))+^(""n)C_(1).(1)/(2^(n))=(n)/(2^(n))`
`P(E_(1)nnE_(2))=("exactly one head and"(n-1)till)`
`=^(""n)C_(1).(1)/(2).(1)/(2^(n-1))=(n)/(2^(n))`
If `E_(1)and E_(2)` are indipendent, then
`P(E_(1)nnE_(2))=P(E_(1)).P(E_(2))`
`implies(n)/(2^(n))=(1-(1)/(2^(n-1)))((n+1)/(2^(n)))`
`impliesn=(1-(1)/(2^(n-1)))(n+1)`