# Doubt from probability

**pushkar_2020**#1

**Tanmay_1**#3

Even number 2,4,6 so p(even)=3/6=1/2

Odd number 1,3,5 so p(odd)=3/6=1/2

Now applying reasoning ...suppose (a+b) to the power 2

Then number of terms=3

(a+b) to the power 5 then nubmer of terms=6

Here given n=odd say 2k+1 so (p-1/2 for odd+p-1/2 for even)

Whole to the power 2k+1

So total number of terms 2k+2

k+1 terms contains even power of odd and k+1 terms contains odd power of odd ...

So probablity (k+1)/(2k+2)=1/2

PLS CHECK IS IT CORRECT REASONING...