Calculate conditional probabilities for coin tosses
Overview
This question evaluates understanding of conditional probability and independence in simple probabilistic experiments. It belongs to the Statistics & Math domain, is commonly asked to assess foundational probabilistic reasoning used in statistical inference and algorithmic decision-making, and targets conceptual understanding with elementary practical computation.
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Sep 6, 2025, 12:00 AM
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Probability with Two Fair Coin Tosses
You toss a fair coin twice. Let the coin be fair (P(H) = P(T) = 1/2) and the tosses independent.
(a) Compute P(second = H | first = T).
(b) Given that at least one of the two tosses is Heads, compute P(both = HH | at least one H). Use an explicit sample space or conditional probability formulas, and explain your reasoning.
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