Question 386746
Let X = r.v. indicating the number of times 3 appears in 4 tries.  Then the possible values of x are 0,1,2,3,4.  This is a binomial experiment with n = 4, p = 1/6, and q = 5/6.  The probability distribution is given by 

{{{p(x) = nCx*(5/6)^(4-x)*(1/6)^x}}}.
The mean is given by {{{mu = np = 4*(1/6) = 2/3}}}, and variance is 
{{{sigma^2 = npq = 4*(1/6)*(5/6) = 5/9}}}.  Thus the standard deviation is {{{sigma = sqrt(5)/3}}}.