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I am starting a probability class and I am a bit confused looking at my textbook. An exercice is mentionning selecting cards randomly when another one says picking balls uniformly at random I have seen that a lot of posts are dealing about this but all of them have not made any sense to me unfortunately...

Could you explain me the difference between the two ? (if there is)

Complementary question :
If an exercice is saying: picking balls uniformly at random
How do I know if we take the four balls at the same time or the balls one by one ?

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    $\begingroup$ The second is more precise than the first, though in practice they are used similarly. Saying that something is done "randomly" is ambiguous as the probability distribution is not specified. Adding "uniformly" tells you the distribution. $\endgroup$
    – lulu
    Nov 8, 2020 at 10:36
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    $\begingroup$ For the second question, I'd say it would depend on context. In many cases, it makes no difference for the problem. As you have noticed, people often phrase these problems informally...some flexibility is required of the reader. $\endgroup$
    – lulu
    Nov 8, 2020 at 10:44
  • $\begingroup$ Thank you for these answers. I agree a lot with you on the second question. The results can be totally different but exercices presented like this are difficult as they do not give a lot of details. If the exercice is like : picked one by one. I instantly know that I will decrease the number of balls from a pick to another $\endgroup$ Nov 8, 2020 at 10:49

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For the second question, you need to know if there is replacement, and when. Each ball replaced is different than all four replaced before the next operation, which is different than no replacement. Combinatorics with replacement is trickier, but Professor Woo on Youtube has excellent videos from 2013.

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