Simple probability question - Cards

[arron77]

You have a deck of cards.

I deal out one card each to 3 people. Is it more likely or less likely that AT LEAST one of the people will be dealt a heart?

I require clarification on this, thanks in advance.

 

[tiny-tim]

welcome to pf!

hi arron77! welcome to pf!

I deal out one card each to 3 people. Is it more likely or less likely that AT LEAST one of the people will be dealt a heart?

in other words: you deal 3 cards: what is the likelihood that at least one will be a heart?

show us how far you've got, and then we'll comment ​

 

[arron77]

well I'm not going into detail this was more to settle a point

player 1 has a 1/4 chance to get a heart, as do the other two players

so combined to me they have a 3/4 chance to get a heart. Thus I should not bet on this game as I would most likely lose

 

[alan2]

If you're new to probability you have to learn to think in an odd way. It is ridiculous to calculate the prob that at least one gets a heart. Try instead the probability that no one gets a heart. You just need to deal from the other 39 cards. Then the prob that at least one gets a heart is 1 minus the prob that nobody gets a heart.

 

[tiny-tim]

player 1 has a 1/4 chance to get a heart, as do the other two players

so combined to me they have a 3/4 chance to get a heart. Thus I should not bet on this game as I would most likely lose

well, that reasoning has to be wrong …

if you dealt 1 card to 4 people, would the probability of at least one heart be 4/4 ?

 

[alan2]

Yes that reasoning is wrong. But the quick answer is that if you deal 1 card each to 3 people then the probability of at least one heart is about 0.59.