Binomial Distribution : Probability equation solution

Question :In a binomial distribution for p=.48, q=1-p=.52 find the population size n1 so that P(X>=3)=.95

My solution :
can be rewrite as
P(X=0)+P(X=1)+P(X=2)=.05 ------------------------------------------ eq(1)
but i am un able to solve the above equation for n1,

Is there any way to solve the equation (1) or is there any alternate solution?
Your equation is correct, but you need to "plug in" the probabilities for X=0, X=1, and X=2. You need to use this: \( \sum_{x = 0}^n {n \choose{x}} p^x (1-p)^{n-x} \)

Assuming you did this, I understand your frustration. The equation is a little messy. Still pondering it.
Last edited: