(a) To find the probability distribution of \(X\), we calculate all possible sums of the numbers from the red and blue spinners and their probabilities:

(b) Given \(E(X) = 0.25\), we use the formula for variance:

\(\text{Var}(X) = E(X^2) - [E(X)]^2\)

Calculate \(E(X^2)\):

\(E(X^2) = \frac{1}{16}(-2)^2 + \frac{3}{16}(-1)^2 + \frac{5}{16}(0)^2 + \frac{5}{16}(1)^2 + \frac{2}{16}(2)^2\)

\(= \frac{1}{16} \times 4 + \frac{3}{16} \times 1 + \frac{5}{16} \times 0 + \frac{5}{16} \times 1 + \frac{2}{16} \times 4\)

\(= \frac{4}{16} + \frac{3}{16} + 0 + \frac{5}{16} + \frac{8}{16} = \frac{20}{16} = 1.25\)

Now, calculate \(\text{Var}(X)\):

\(\text{Var}(X) = 1.25 - (0.25)^2 = 1.25 - 0.0625 = 1.1875\)