If four cards are drawn from a standard deck of 52 playing cards and not replaced?

, find the probability of getting at least one heart.





I've been trying to figure this out for an hour and it's the last question on my stat hw. I'm sure I'm making it much harder than it actually is, but help would be greatly appreciated! Thanks.

If four cards are drawn from a standard deck of 52 playing cards and not replaced?
Look at this backwards. The probability of getting at least one heart is 1 minus the probability that you get no hearts at all.





Probability that first card is not a heart = 39/52


Probability that second card is not a heart = 38/51


Probability that third card is not a heart = 37/50


Probability that fourth card is not a heart = 36/49





Multiply (these are independent probabilities) = 6327/20825





1 - 6327/20825 = 14498/20825 approx 70% chance
Reply:P(w/o replacing, 4 cards drawn, at least one heart)


= 1 -- P(no hearts drawn)


= 1 -- 39/52*38/51*37/50


= 1 -- 54834/132600


= 77766/132600


= 0.5865
Reply:so the possibility of the four cards being a heart is 13/52


so 13-4=9


so


9/52?


im not sure but i think so


good luck(:
Reply:you got a 25% chance of drawing a heart
Reply:1/13
Reply:as long as you don`t know which card this 4 are,


make no different .





13 /52 = 1 /4
Reply:The probability or getting at least one heart would be a 1 in 4 cance because the deck of 52 is split evenly with 13 hearts, 13 diamonds, 13 clubs and 13 spades. so the answer is 1 in 4 or 25%