What is the probability of randomly drawing a queen given that it is a face card from a well-shuffled 52 card deck?

Ok So If you’re drawing a queen from a pile consisting of ONLY face cards, the probability of drawing a queen is 4/12 (4 queens, 4 kings, 4 jacks). This reduces to 1/3, or 0.3333, or 33%.

Now, if you’re drawing a queen from a standard deck of cards (52 in all), the probability is different. There are still only 4 queens in the deck of 52: 4/52. This reduces to 1/13, or 0.0769, or 7.7%

The probability of drawing a queen from a deck of ONLY face cards is much higher (33%) than drawing a queen from a standard deck of cards (7.7%).Playing cards include thirteen ranks of each of the four suits: clubs (♣), diamonds (♦), hearts (♥) and spades (♠). Each suit includes three face cards a king, queen & jack.

Therefore, in total there are 12 face cards (3 face cards of each suit × 4 suits).

Each suit has one queen face and there are 4 suits. So, the deck contains 4 queen face. Number of event, n(E)=4 & number of all possible events, n(s)=12.

Therefore

P(E)=n(E)/n(s)=4/12=1/3

Step-by-step explanation: