In a deck of 52 playing cards what is the probability of drawing a club card, and then a second club card without replacement

Answer 1

To find the probability of drawing a club card and then a second club card without replacement, we need to first calculate the probability of drawing a club card on the first draw, and then multiply it by the probability of drawing a club card on the second draw.

There are 13 club cards in a deck of 52 playing cards, so the probability of drawing a club card on the first draw is 13/52.

Once a club card is drawn, there are 12 club cards left in a deck of 51 playing cards for the second draw. Therefore, the probability of drawing a club card on the second draw, without replacement, is 12/51.

To find the overall probability, we need to multiply both probabilities together:

(13/52) * (12/51)

Simplifying this expression gives us the final probability:

(1/4) * (4/17) = 4/68 = 1/17

Therefore, the probability of drawing a club card and then a second club card without replacement is 1/17.