Simple probability question - Cards

In summary: This is because there are 13 hearts in a deck of 52 cards, so the probability of any one person getting a heart is 13/52 or 1/4. This means the probability of all three people not getting a heart is (3/4)^3 or about 0.42. Since the probability of no one getting a heart is about 0.42, the probability of at least one person getting a heart is 1 - 0.42 or about 0.59. In summary, the probability of at least one person getting a heart when dealing one card each to three people is about 0.59.
  • #1
arron77
2
0
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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  • #2
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:
 
  • #3
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
 
  • #4
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.
 
  • #5
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:
 
  • #6
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.
 

FAQ: Simple probability question - Cards

What is simple probability?

Simple probability is the likelihood of a specific event occurring, expressed as a fraction or decimal. It is based on the assumption that all outcomes are equally likely to happen.

How is probability calculated?

Probability is calculated by dividing the number of desired outcomes by the total number of possible outcomes. For example, if you want to find the probability of drawing a heart from a deck of cards, the calculation would be 13 (number of hearts) divided by 52 (total number of cards) which equals 1/4 or 0.25.

What is a deck of cards?

A deck of cards is a set of 52 playing cards divided into four suits (hearts, diamonds, spades, and clubs) and ranks (Ace, 2-10, Jack, Queen, and King). Each suit contains 13 cards.

What is the difference between a standard deck of cards and a deck of playing cards?

A standard deck of cards and a deck of playing cards are both made up of 52 cards, but a standard deck is typically used for playing traditional card games while a deck of playing cards may have unique designs or be used for specific games.

How is a deck of cards used in probability?

A deck of cards is often used to demonstrate simple probability questions by representing different outcomes with different cards. It can also be used to simulate larger sampling sizes by shuffling and drawing multiple times.

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