Final answer:
The key concepts of Example 16 in an algebra two probability unit are combinations and binomial coefficients, where the binomial theorem helps to expand expressions like (a + b)^n and calculate probabilities using binomial distributions.
Step-by-step explanation:
The key concepts covered in Example 16 of an algebra two probability unit, which illustrates combinations and the binomial theorem, are b) Combinations and binomial coefficients. Combinations involve selecting items from a group without regard to the order in which they are selected, and this is expressed mathematically as the number of k-combinations from a given set of n elements. Moreover, the binomial theorem provides a way to expand expressions that are raised to a power, such as (a + b)n, and is associated with binomial coefficients which can be found in Pascal's triangle or calculated using factorials.
The binomial probability distribution is applicable when an experiment satisfies certain conditions: there are a fixed number of trials (n), each trial has only two possible outcomes (success or failure), the probability of success (p) is constant for each trial, and the trials are independent. The mean (μ) and standard deviation (σ) of a binomial distribution can be calculated using the formulas μ = np and σ = √npq respectively. The binomial theorem is an essential part of understanding the math behind probability and is key in various fields, including complex and quantum mechanical systems, indicated by Big Idea 7. When working with probability, the product rule and sum rule can be applied to find the probability of independent or combined events occurring.