If X and Y are independent fair coins, what is P(X=heads and Y=heads)?

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Prepare for the AMSOC 26-003 Module A Test. Utilize flashcards and multiple choice questions with hints and explanations. Ace your exam!

Multiple Choice

If X and Y are independent fair coins, what is P(X=heads and Y=heads)?

Explanation:
When events are independent, the chance both happen is the product of their individual chances. Each fair coin lands heads with probability 1/2, so both coins landing heads is (1/2) × (1/2) = 1/4. Think of the four equally likely outcomes when flipping two coins: heads-heads, heads-tails, tails-heads, tails-tails. Only one of these outcomes is both heads, which corresponds to probability 1/4. The other options would represent either a single-coin chance (1/2), certainty (1), or impossibility (0).

When events are independent, the chance both happen is the product of their individual chances. Each fair coin lands heads with probability 1/2, so both coins landing heads is (1/2) × (1/2) = 1/4. Think of the four equally likely outcomes when flipping two coins: heads-heads, heads-tails, tails-heads, tails-tails. Only one of these outcomes is both heads, which corresponds to probability 1/4. The other options would represent either a single-coin chance (1/2), certainty (1), or impossibility (0).

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