Let the probability of receiving an elephant be \(\frac{1}{5}\) and the probability of not receiving an elephant be \(\frac{4}{5}\).

We need to find the probability that the first elephant is received before the 6th Monday, i.e., \(P(X < 6)\).

Method 1:

Calculate \(P(X \leq 5) = 1 - (0.8)^5\).

\(P(X \leq 5) = 1 - 0.8^5 = 0.672\).

Method 2:

Calculate \(P(X < 6) = P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)\).

\(P(X = 1) = \frac{1}{5}\).

\(P(X = 2) = \left( \frac{4}{5} \right) \times \frac{1}{5}\).

\(P(X = 3) = \left( \frac{4}{5} \right)^2 \times \frac{1}{5}\).

\(P(X = 4) = \left( \frac{4}{5} \right)^3 \times \frac{1}{5}\).

\(P(X = 5) = \left( \frac{4}{5} \right)^4 \times \frac{1}{5}\).

Summing these probabilities gives \(0.672\).