Simple probability question - Cards

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When dealing one card each to three people from a standard deck of cards, the probability that at least one person receives a heart is approximately 0.59. The initial reasoning that the combined chance of three players getting a heart is 3/4 is incorrect. Instead, it's more effective to calculate the probability that none of the players receive a heart, which involves considering the remaining 39 cards. The discussion emphasizes the importance of understanding probability concepts, particularly in calculating complementary probabilities. Ultimately, the likelihood of at least one heart being dealt is significant enough to warrant consideration in betting scenarios.
arron77
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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.
 
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welcome to pf!

hi arron77! welcome to pf! :wink:
arron77 said:
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 :smile:​
 
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
 
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.
 
arron77 said:
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 :redface: …

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

Thread 'Formal derivation of statement from Peano Arithmetic system'

I was reading a Bachelor thesis on Peano Arithmetic (PA). PA has the following axioms (not including the induction schema): $$\begin{align} & (A1) ~~~~ \forall x \neg (x + 1 = 0) \nonumber \\ & (A2) ~~~~ \forall xy (x + 1 =y + 1 \to x = y) \nonumber \\ & (A3) ~~~~ \forall x (x + 0 = x) \nonumber \\ & (A4) ~~~~ \forall xy (x + (y +1) = (x + y ) + 1) \nonumber \\ & (A5) ~~~~ \forall x (x \cdot 0 = 0) \nonumber \\ & (A6) ~~~~ \forall xy (x \cdot (y + 1) = (x \cdot y) + x) \nonumber...
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