Calculate conditional probabilities for coin tosses
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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.
Consider two independent tosses of a fair coin. (a) What is the probability that the second toss is Heads given that the first toss was Tails, P(second=H | first=T)? (b) Given that at least one of the two tosses is Heads, what is the probability that both tosses are Heads, P(both=HH | at least one H)? Explain using an explicit sample space or conditional probability formulas.
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