a) List pairs for sum 6:

\( (2, 4), (3, 3), (4, 2) \) [3]

b) Determine probabilities from distribution:

\( p = \frac{1}{16} \)

\( q = \frac{2}{16} \)

\( r = \frac{2}{16} \) [3]

c) Use binomial distribution:

Let \( X \) be the number of times the sum is 5

\( X \sim \text{B}(4, 0.25) \)

Fred wins if \( P(X \geq 3) \)

\( P(X = 3) = \binom{4}{3} \times 0.25^3 \times 0.75^1 \)

\( = 4 \times 0.015625 \times 0.75 = 0.046875 \)

\( P(X = 4) = 0.25^4 = 0.00390625 \)

\( P(X \geq 3) = 0.046875 + 0.00390625 = 0.05078125 \)

Rounded to 4 decimal places:

\( \approx 0.0508 \) [6]