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What is the difference between the following statements:(or are they the same)

Statement 1: What is the probability of king of spades being the 10th card

Statement 2: What is the probability of the 10th card being the king of spades

(Considering the regular pack of 52 cards)

Ash_Tag
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    Why do you think there even is a difference? – Dominique Sep 21 '23 at 11:09
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    This is an occurrence of the commutativity of the equality relation in natural language – H. sapiens rex Sep 21 '23 at 11:29
  • If the statements were same (as mentioned in the comments) why are the results claimed by this book different. I am seriously confused.

    Image source: Challenges and Thrills of Pre College Mathematics: By V Krishnamurthy [1]: https://i.stack.imgur.com/TIj5z.jpg

     – Ash_Tag Sep 21 '23 at 13:17
  • The numbers in your image... $\left(1-\frac{1}{52}\right)^9\times\frac{1}{52}$ correspond to if the dealing was done with replacement, that the first occurrence of a king of spades is the tenth time drawing from the deck, where the result of each draw is independent of one another (i.e. after each draw is revealed, it is shuffled back into the deck and another random card (possibly the same) is revealed for the next draw). This is typically not what is meant when we say "a deck of cards is dealt out" which makes me think the book is simply wrong. – JMoravitz Sep 21 '23 at 14:14
  • Under the typical meanings of the words in the question, both problems should have had an answer of $\frac{1}{52}$. – JMoravitz Sep 21 '23 at 14:16
  • I would not be surprised if there are additional errors in the book related to multiplying probabilities that should not be multiplied. Be warned that $\Pr(A\cap B) = \Pr(A)\times \Pr(B)$ is true if and only if the events $A$ and $B$ are independent. The results of draws from a deck without replacement are one of the most basic examples of non-independent events, and it is frankly embarrassing that a book could get this wrong. – JMoravitz Sep 21 '23 at 14:18

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