Probability using a deck o' cards

In summary, the conversation discusses the probability of drawing all four aces before any of the tens in a shuffled deck of cards. The problem involves without replacement and the initial probability of drawing an ace is 4/52. The conversation also mentions a similar problem involving the binomial theorem and finding the probability of drawing five red cards without replacement. A suggestion is given to consider a deck with only 8 cards, 4 aces and 4 tens.
  • #1
satchmo05
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Homework Statement


A deck of cards is shuffled and the cards are turned up one at a time. What is the probability that all the aces will appear before any of the tens?


Homework Equations


No equations that I know of are useful here...


The Attempt at a Solution


This problem is one that deals without replacement due to the unspoken assumption. Ergo, the initial probability of drawing an ace off the top of the deck is 4/52. I am not sure where to go from here. I have a similar problem concerning drawing 10 cards and finding the probability of drawing five red cards without replacement. This example uses the binomial theorem, but I am having a hard time using that theorem here...

Any helpful suggestions? Thanks for your time and help in advance! Much appreciated!
 
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  • #2
Do the other cards in the deck really matter? Suppose there are just 8 cards, 4 aces and 4 tens?
 

FAQ: Probability using a deck o' cards

1. What is the probability of drawing a specific card from a deck?

The probability of drawing a specific card from a deck of 52 cards is 1/52, or approximately 1.92%. This is because there is only one specific card out of 52 cards in the deck.

2. What is the probability of drawing a card of a certain suit?

The probability of drawing a card of a certain suit (clubs, diamonds, hearts, or spades) from a deck of 52 cards is 1/4, or 25%. This is because there are 13 cards of each suit in a deck of cards.

3. What is the probability of drawing a face card (jack, queen, king) from a deck?

The probability of drawing a face card from a deck of 52 cards is 12/52, or approximately 23.08%. This is because there are 12 face cards (4 jacks, 4 queens, and 4 kings) in a deck of cards.

4. What is the probability of drawing a red card from a deck?

The probability of drawing a red card from a deck of 52 cards is 26/52, or 50%. This is because there are 26 red cards (13 hearts and 13 diamonds) in a deck of cards.

5. What is the probability of drawing a pair of cards with the same number or face value?

The probability of drawing a pair of cards with the same number or face value (e.g. two 5s or two queens) from a deck of 52 cards is 3/51, or approximately 5.88%. This is because there are 3 other cards with the same number or face value as the first card drawn, and 51 total cards left in the deck after the first card is drawn.

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