Probability using a deck o' cards

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SUMMARY

The probability problem discussed involves determining the likelihood that all four aces in a standard deck of 52 cards appear before any of the four tens. The initial probability of drawing an ace first is calculated as 4/52. The discussion highlights the complexity of this problem, particularly in the context of drawing without replacement and the relevance of the binomial theorem, although its application remains unclear for this specific scenario.

PREREQUISITES
  • Understanding of basic probability concepts
  • Familiarity with combinatorial mathematics
  • Knowledge of the binomial theorem
  • Experience with probability problems involving drawing without replacement
NEXT STEPS
  • Study the concept of conditional probability in card games
  • Explore combinatorial approaches to probability problems
  • Learn about the application of the binomial theorem in various scenarios
  • Investigate probability distributions related to card draws
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Students studying probability, mathematicians interested in combinatorial problems, and educators teaching probability concepts through practical examples.

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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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Do the other cards in the deck really matter? Suppose there are just 8 cards, 4 aces and 4 tens?
 

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