# Three cards are randomly drawn from a standard deck of 52-playing cards without replacement. What is the probability of drawing three queens?

Mar 27, 2018

~~0.00018=0.018%

#### Explanation:

For the first draw, there are 52 cards, so that is your denominator and because you have four queens in the deck, this is your nominator. Therefore, the probability of the first draw is $\frac{4}{52} = \frac{1}{13}$

For the second draw, there are 51 cards with three queens left. Therefore the probability is $\frac{3}{51} = \frac{1}{17}$

For the third draw, there are 50 cards with two queens left. Therefore the probability is $\frac{2}{50} = \frac{1}{25}$

All in all, the probability is the product of those probabilities.
$\frac{1}{13} \cdot \frac{1}{17} \cdot \frac{1}{25} \approx 0.00018$

Mar 27, 2018

1/5525~~0.018%

#### Explanation:

The probability of drawing a queen in the first turn is $\frac{4}{52}$ (four queens and 52 cards) $\frac{4}{52} = \frac{1}{13}$

If this is the case, than there are 51 cards and three of them are queens. Therefore the probability is $\frac{1}{13} \cdot \textcolor{b l u e}{\frac{3}{51}} = \frac{1}{13} \cdot \frac{1}{17} = \frac{1}{221}$

If this is the case, than there are 50 cards left and two of them are queens. Therefore the probability to draw 3 queens in a row is

$\frac{1}{221} \cdot \textcolor{b l u e}{\frac{2}{50}} = \frac{1}{221} \cdot \frac{1}{25} = \frac{1}{5525}$