Final answer:
The question is focused on the mathematical concept of probability distribution, in particular the binomial distribution. College-level understanding is required to calculate probabilities of outcomes and the expected profit in games of chance using the binomial formula.
Step-by-step explanation:
The subject of the question pertains to the concept of probability distribution, more specifically the binomial distribution. This is a part of probability theory and statistics, which is a mathematical discipline. The question seems to be at the college level, as it involves a deeper understanding of probability distributions and mathematical calculations.
In the given examples, the calculation of probabilities for various outcomes of drawing cards or rolling dice involves the use of the binomial distribution formula, where n represents the number of trials, p represents the probability of success in a single trial, and q represents the probability of failure. The mean of a binomial distribution is calculated using μ = np, and the standard deviation is σ = √npq. When applying this to gambling or games of chance, the expected profit can be calculated based on the probability of winning and the potential payouts.