Why Is Calculating Card Probabilities Confusing?

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SUMMARY

The probability of drawing a card from a standard 52-card deck that is divisible by 4 is correctly calculated as 12/52, simplifying to 3/13. The confusion arises from misinterpreting the total number of cards divisible by 4, which includes the 4, 8, and 12 (King) values across all suits. For the second problem, the correct probability of drawing a card divisible by 10 or 11 is indeed 8/52, simplifying to 2/13, as there are 4 cards for each value in the deck.

PREREQUISITES
  • Understanding of basic probability concepts
  • Familiarity with standard deck of playing cards
  • Knowledge of divisibility rules
  • Ability to simplify fractions
NEXT STEPS
  • Study the concept of probability in combinatorial contexts
  • Learn about the properties of divisibility in number theory
  • Explore more complex probability problems involving card games
  • Review the fundamentals of fractions and their simplification
USEFUL FOR

Students studying probability, educators teaching combinatorial mathematics, and anyone interested in understanding card game strategies and outcomes.

lorik
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Homework Statement


From 52 cards we draw one .Whats the probability that the drawn card is divisible by 4

Now : in my notebook its 12/52=3/13 .But shouldn't it be 13/52 ? BECAUSE clearly if we multiply 13 *4=52

Same problem : Whats the probability that of 52 cards I draw one that is divisible
with 10 or 11 .In notebook its like this P(a)+p(b)= 4/52+4/52=8/52=4/26=2/13

BUT shouldn't this as well be 5/52+5/52


Homework Equations





The Attempt at a Solution



PLEASE just tell the correct answer every time I post here somebody argues about pointless stuff and leaves me hanging with no clue !??

Sorry second problem fixed so 4/52+5/52 is correct ?
 
Last edited:
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lorik said:

Homework Statement


From 52 cards we draw one .Whats the probability that the drawn card is divisible by 4

Now : in my notebook its 12/52=3/13 .But shouldn't it be 13/52 ? BECAUSE clearly if we multiply 13 *4=52

Same problem : Whats the probability that of 52 cards I draw one that is divisible
with 10 or 11 .In notebook its like this P(a)+p(b)= 4/52+5/52=8/52=4/26=2/13

BUT shouldn't this as well be 5/52+5/52


Homework Equations





The Attempt at a Solution



PLEASE just tell the correct answer every time I post here somebody argues about pointless stuff and leaves me hanging with no clue !??

On the first one, your book is correct that there are 12 cards in the deck that have a value that is divisible by 4. What cards of each suit have a value that is divisible by 4?
 

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