(a) The probability that Kayla takes more than 6 throws to achieve a success is given by the geometric distribution formula:

\(P(X > 6) = (0.75)^6\)

Calculating this gives:

\(P(X > 6) = 0.178\)

(b) To find the probability that Kayla achieves at least 3 successes in 10 throws, we use the binomial distribution:

\(1 - P(0, 1, 2) = 1 - \left( (0.75)^{10} + \binom{10}{1} (0.25)^1 (0.75)^9 + \binom{10}{2} (0.25)^2 (0.75)^8 \right)\)

Calculating each term:

\((0.75)^{10} = 0.0563135\)

\(\binom{10}{1} (0.25)^1 (0.75)^9 = 0.1877117\)

\(\binom{10}{2} (0.25)^2 (0.75)^8 = 0.2815676\)

Summing these gives:

\(0.0563135 + 0.1877117 + 0.2815676 = 0.5256\)

Thus,

\(1 - 0.5256 = 0.474\)