Cards are drawn one by one at random from a well shuffled pack of 52 cards until 2 aces are obtained. The probability that 18 draws are required for this is

For the 18th draw to yield the second ace, the first 17 draws must contain exactly 1 ace and 16 non-aces, followed by 1 of the remaining 3 aces on the 18th draw. The probability of drawing 1 ace and 16 non-aces in the first 17 draws is calculated using combinations as (4C1 times 48C16) divided by 52C17. Multiply this by the probability of drawing an ace on the 18th draw, which is 3 divided by 35, to get the final result of 561/15925.

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