SOLUTION: Hi there, I am trying to work out the following: 52 card deck without replacement. 4 players 1 card each. First player has a heart. Each of the other 3 players get a card. What

Question 838663: Hi there,
I am trying to work out the following: 52 card deck without replacement. 4 players 1 card each. First player has a heart. Each of the other 3 players get a card. What are the chances of ANY of the other 3 cards being a heart (or how do you work it out).
This was where I got to: Second player: probability is 12/51 (twelve hearts left with 51 cards), Third player 12/50, Fourth 12/49. How do I determine the probability of ANY of the other players having a HEART?
What do I do with these numbers - 0.2352941176470588, .24,
0.2448979591836735 ?
If I wanted to find out what was the probability of them ALL being HEARTS I would multiply these numbers (I think)
Would you recommend any text book / accessible material on this type of probability question?
Thanking you in advance
Kyran
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
52 cards, 13 Hearts, 39 Non-Hearts
First player - Heart
51 cards, 12 Hearts, 39 Non-Hearts
Look at the possible draws of the next three cards (H - heart, N - non-heart) and calculate the probabilities of each, they are all independent events.
NNN-
NNH-
NHN-
NHH-
HNN-
HNH-
HHN-
HHH-
If you sum up all of the probabilities, they do add up to 1. They must, these are the only possible draws.
Now look for the ones that have at least 1 heart.
Or look for the one that has no hearts and subtract from 1.
P(at least 1 heart)=
Yes, all of them being hearts would be HHH,
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