Simple probability question - Cards

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Discussion Overview

The discussion revolves around a probability question concerning the likelihood of at least one person being dealt a heart when three cards are dealt from a standard deck of cards. Participants explore different approaches to calculating this probability, including direct and complementary methods.

Discussion Character

  • Exploratory
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant asks whether it is more or less likely that at least one of three people will be dealt a heart.
  • Another participant suggests calculating the probability of at least one heart by first determining the probability that no one receives a heart, proposing a complementary approach.
  • Some participants assert that each player has a 1/4 chance of receiving a heart, leading to a combined probability of 3/4, which is challenged by others.
  • A later reply indicates that the probability of at least one heart being dealt is approximately 0.59, but does not clarify how this was derived.

Areas of Agreement / Disagreement

Participants express disagreement regarding the correct method to calculate the probability, with some advocating for direct calculation and others for the complementary approach. There is no consensus on the reasoning or the final probability value.

Contextual Notes

Some participants' reasoning appears to rely on assumptions about the distribution of cards and the independence of events, which may not be fully articulated. The discussion reflects varying levels of understanding of probability concepts.

Who May Find This Useful

This discussion may be useful for individuals interested in probability theory, particularly those looking to understand different methods of calculating probabilities in card games.

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.
 

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