The correct answer is:

b. Probability Theory & Statistical Inference

Explanation:

When analyzing statistical outcomes for a coin flip, the primary mathematical skills involved are rooted in Probability Theory, which examines the likelihood of each outcome in a coin flip (heads or tails) and calculates the probabilities associated with different sequences of flips. In some cases, Statistical Inference could also be used if we’re drawing conclusions from observed data (such as analyzing a series of coin flips and determining biases).

Here's how the other options fit or don’t fit:

• a. Recursive Functions and Sequences: Not applicable here, as coin flips are independent events without a recursive sequence.
• c. Linear Algebra: Not needed, as coin flips don't involve vectors or matrices.
• d. Recursive Functions and Sequences & Combinatorics: While combinatorics could be relevant, recursive functions and sequences aren’t, so this combination is not suitable.

Let me know if you'd like more details on calculating probabilities for coin flips!

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Here are five related questions to deepen your understanding:

1. What is the probability of getting exactly 3 heads in 5 coin flips?
2. How can we use the binomial distribution for predicting outcomes in multiple coin flips?
3. What is the likelihood of a fair coin landing heads 10 times in a row?
4. How do we determine if a coin is biased based on flip results?
5. How does the law of large numbers apply to coin flips?

Tip: In probability theory, understanding independent vs. dependent events is key; coin flips are typically independent, meaning each flip does not affect others.