Question

Calculate the probability of winning: Draw 2 cards from a standard deck of cards without replacement. You win if you draw a face card, then a number card in that order. Do not count Aces as face cards. Round answer to three decimal places.

Answer 1

The formula to calculate the probability of an event is given to be:

$P=\frac{number\text{ }of\text{ }successful\text{ }events}{number\text{ }of\text{ }total\text{ }events}$

There are 12 face cards in a standard deck and 36 number cards. A standard deck has 52 cards.

First Pick: A face card

$P=\frac{12}{52}=\frac{3}{13}$

Second Pick: A number card

Without replacement, there will be 51 cards left in the deck. Therefore, the probability is:

$P=\frac{36}{51}=\frac{12}{17}$

Therefore, the combined probability will be:

$\begin{gathered} P=\frac{3}{13}\times\frac{12}{17}=\frac{36}{221} \\ P\approx0.163 \end{gathered}$

The probability is 0.163.