Probability a five-card contains the ace of hearts

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In summary, the probability of drawing the ace of hearts in a five-card hand is 1 out of 52, or approximately 1.92%. If one card in the hand is already known to be the ace of hearts, the probability decreases to 1 out of 51, or approximately 1.96%. The probability of drawing the ace of hearts is not the same for every five-card hand and can be influenced by factors such as the number of cards and aces of hearts in the deck. To calculate the probability of getting multiple aces of hearts in a five-card hand, the formula for combination probability must be used. Previous draws do not influence the probability of drawing the ace of hearts as each draw is independent.
  • #1
zbobet2012
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Homework Statement


What is the probability that a five-card contains the ace of hearts?

Homework Equations


[tex]P(E)=|E|/|S|[/tex]
[tex]P(E_{1}\bigcup E_{2})=P(E_{1})+P(E_{2}) + P(E_{1}\bigcap E_{2})[/tex]

The Attempt at a Solution


The number of ways to choose 5 cards from 52*the numbers of ways to get an ace from five of those?
[tex]C(52,5)C(5,1)[/tex]
 
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  • #2
mmm, try:

number of ways to choose ace of hearts*number of ways to choose the other 4 cards/number of ways to choose 5 cards from 52.

1*c(51,4)/c(52,5)

that seems better to me.
 
  • #3
That looks better, thank you very much.
 

1. What is the probability of drawing the ace of hearts in a five-card hand?

The probability of drawing the ace of hearts in a five-card hand is 1 out of 52, or approximately 1.92%. This is because there are 52 cards in a deck and only 1 ace of hearts.

2. How does the probability change if I already know that one card in the hand is the ace of hearts?

If you already know that one card in the hand is the ace of hearts, the probability of drawing it in a five-card hand decreases. This is because there are now only 51 cards remaining in the deck, and only 4 aces of hearts left. The new probability is 1 out of 51, or approximately 1.96%.

3. Is the probability of drawing the ace of hearts the same for every five-card hand?

No, the probability of drawing the ace of hearts is not the same for every five-card hand. It depends on the number of cards in the deck, the number of aces of hearts in the deck, and the number of cards in the hand. For example, if there are multiple decks being used, the probability will be different compared to a single deck being used.

4. How do I calculate the probability of getting multiple aces of hearts in a five-card hand?

To calculate the probability of getting multiple aces of hearts in a five-card hand, you would need to use the formula for combination probability. This takes into account the number of ways to arrange the aces of hearts in the hand and the total number of possible five-card hands. The result will be a decimal, which can then be converted to a percentage.

5. Can the probability of drawing the ace of hearts be influenced by previous draws?

No, the probability of drawing the ace of hearts cannot be influenced by previous draws. Each draw is independent and the probability remains the same. For example, if the ace of hearts was drawn in a previous hand, the probability of drawing it in the next hand will still be 1 out of 52, regardless of what was drawn in the previous hand.

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