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I am struggling to grasp conditional probability as it is something I never fully understood in school. Could anyone explain to me how to answer the following questions? I know how to do a few of them but still confused by the others.

Two cards are chosen without replacement from a 52 card deck. In each case, find the conditional probability both cards are aces.

(a) If you are told one of the cards is the ace of spades.

(b) If you are told one of the cards is an ace.

(c) If you are told one of the cards is a spade.

(d) if you are told the first card selected is an ace.

(e) If you are told the second card selected is an ace.

Find the probability of getting four of a kind, given you have the ace of hearts and the ace of diamonds.

If anyone could help me in developing an understanding of this topic that would be brilliant

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    Which ones do you know how to do (and what do you think the answers are?). This may help people understand where the gaps are in your knowledge – lioness99a Feb 24 '20 at 15:27
  • I would also recommend Khan Academy as a good resource for learning topics outside of a school setting – lioness99a Feb 24 '20 at 15:28
  • I can do the first two, I think I got 1/221 for part (a) and 1/33 for part (b) –  Feb 24 '20 at 15:31
  • Sorry that was a question but the answer must be zero, I changed it to 4 of a kind –  Feb 24 '20 at 15:32
  • You should also indicate that you are speaking of an ordinary $5$ card hand (assuming that's what you intended). – lulu Feb 24 '20 at 15:33
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    Why not edit your question to include your efforts? Explain where you got $\frac 1{221}$ for instance. It will make it a lot easier to advise you if we see how you are reasoning. – lulu Feb 24 '20 at 15:34
  • Duplicate of the first two parts: Intuition on probability of drawing two aces given that the first draw is an ace. The remaining parts can follow using similar techniques. – JMoravitz Feb 24 '20 at 15:52
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    As for an answer of $\frac{1}{221} = \frac{1}{13\times 17} = \frac{4}{52}\times \frac{3}{51}$... that is the probability of having gotten two aces in general without any conditional statement being considered. If we are told one of the cards is the ace of spades... of course it is more likely that we got two aces. This should be obvious since if we were told something else, such as that one of the cards was a Jack, then we obviously can not have two aces. – JMoravitz Feb 24 '20 at 15:57

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