First slide

Theorems of probability

Question

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

Moderate

A

3/34
B

17/455
C

561/15925
D

none of these

Solution

18 draws are required for 2 aces. This means in the first 17 draws, there is one ace and 16 other cards, and 18th draw produces an ace. So, the required probability is
$\frac{48 C_{16} \times^{4} C_{1}}{^{52} C_{17}} \times \frac{3}{35} = \frac{561}{15925}$

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