Question

Find the probability of getting 2 face cards (king, queen, or jack) when 2 cards are drawn from a deck without replacement.

Answer 1

The probability of drawing 2 face cards from a deck without replacement is calculated by multiplying the probability of the first and second draws, which gives approximately 0.0433 when rounded to four decimal places.

Step-by-step explanation:

To find the probability of drawing 2 face cards from a standard 52-card deck without replacement, we need to calculate the probability of drawing the first face card and then multiply it by the probability of drawing a second face card after the first has been drawn.

There are 12 face cards in total (4 J's, 4 Q's, and 4 K's for each suit), so the probability of drawing one face card on the first draw is 12/52. After drawing one face card, there are now 51 cards left in the deck, and only 11 face cards. The probability of drawing a second face card is now 11/51.

To get the overall probability, we multiply the two probabilities together:

P(First Face Card) × P(Second Face Card | First is a Face Card) = (12/52) × (11/51)

So the probability is:

(12/52) × (11/51) = 0.0433 (rounded to four decimal places)

Answer 2

Well, there are 3 face cards in each suit, so, 12 face cards in total.

P(first card) = 12/52

P(second card)=11/51

P(both) = 12/52 * 11/51

P = 132/2652

Let's write it in the simplest form:

P=11/221