Determine the probability of a discrete random variable

Hello everyone,

I'm really struggling with this homework problem, I'm not really sure what to do:

Quote:

Suppose the population comes from a random variable x = 1, 2, 3, 4, 5, 6 with population probabilitiesp(1)=p(2) and p(3)=p(4)=p(5)=p(6).

Let x_{1},..., x_{n}be a random sample from this population. If the variance σ^{2}= 3 and a random sample of n=21 is drawn, then

P( | x | > 3.6311) is:

**Hint:** You may wish to use the fact that

σ^{2} = ∑(x-μ)^{2}p(x)= ∑x^{2}p(x) - μ^{2}

I know first we must figure the two probabilities: here's one of the formulas you can use in a system of equations:

2x+4y=1

not sure what else to do.. any ideas?