## Set the cell probabilities here.
p11 = 0.2
p12 = 0.3
p21 = 0.1
p22 = 0.4

## Cumulative probabilities.
c1 = p11
c2 = c1+p12
c3 = c2+p21
c4 = c3+p22

## Simulate a contingency table.
U = runif(1e4)
N = array(0, c(2,2))
N[1,1] = sum(U <= c1)
N[1,2] = sum( (U > c1) & (U <= c2) )
N[2,1] = sum( (U > c2) & (U <= c3) )
N[2,2] = sum(U > c3)