If you pick two cards from a standard deck, what is the probability that both are diamonds?

Instruction: Calculate the probability without replacement.

Context: This question assesses the candidate's ability to calculate probabilities in scenarios involving combinations without replacement.

Updated

Official answer

For two uniform draws without replacement, the first card is a diamond with probability 13/52. Given a diamond first, 12 diamonds remain among 51 cards. Thus P(both diamonds) = (13/52)(12/51) = 1/17, about 5.88%.

The draws are dependent; the multiplication rule uses the conditional second probability. The equivalent unordered count is C(13,2)/C(52,2). Squaring 1/4 would give 1/16, appropriate to independent draws with replacement instead.

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