The binomial probability distribution for $n = 5$ trials and a probability of success $p = 0.528$ on a single trial is as follows:

• $P(X = 0) = 0.0234$
• $P(X = 1) = 0.1310$
• $P(X = 2) = 0.2932$
• $P(X = 3) = 0.3279$
• $P(X = 4) = 0.1834$
• $P(X = 5) = 0.0410$

These probabilities sum to 1, confirming the validity of the distribution.

Would you like more details or have any questions?

Here are some follow-up questions to explore further:

1. What is the expected value of the binomial distribution in this case?
2. How would you compute the variance and standard deviation of this distribution?
3. What is the cumulative probability of getting at most 3 successes?
4. How does changing $p$ to a lower or higher value affect the distribution shape?
5. Can you derive the moment-generating function for a binomial distribution?

Tip: In binomial distributions, the probability of success $p$ and the number of trials $n$ significantly influence the skewness of the distribution.