Let the random variable \(X\) represent the number of boxes containing more jellies than chocolates. \(X\) follows a binomial distribution with parameters \(n = 10\) and \(p = 0.64\).

We need to find \(P(X \leq 7)\), which is equivalent to \(1 - P(X \geq 8)\).

Calculate \(P(X \geq 8) = P(X = 8) + P(X = 9) + P(X = 10)\).

Using the binomial probability formula:

\(P(X = 8) = \binom{10}{8} (0.64)^8 (0.36)^2\)

\(P(X = 9) = \binom{10}{9} (0.64)^9 (0.36)^1\)

\(P(X = 10) = \binom{10}{10} (0.64)^{10}\)

Calculate each probability:

\(P(X = 8) = 0.164156\)

\(P(X = 9) = 0.064852\)

\(P(X = 10) = 0.11529\)

Sum these probabilities: \(P(X \geq 8) = 0.164156 + 0.064852 + 0.11529 = 0.344298\)

Therefore, \(P(X \leq 7) = 1 - 0.344298 = 0.759\).