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Let's suppose that I am playing a card game with 3 other friends. One of my friends is on my team while the other 2 people are on the opposing team. The cards have just been shuffled and dealt so that each player now has 13 cards and there are 5 cards still in the deck. There is one wild card in the deck while the rest of the cards are numbered cards of one of the four suits (red, green, yellow, black). I am looking at my cards and I see that I have 4 of the 14 red cards.

Now, for the question. What is the average number of red cards that each of my opponents might have? What about my team-mate? What is the average number of red cards left in the deck?

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up vote 6 down vote accepted

Out of the $44$ cards you don't have, $10$ are red. Your opponents' cards, your teammate's cards and the left-over cards all have the same chance of $10$ in $44$ of being red, so the average number of red cards on each hand is $13\cdot\frac{10}{44}=\frac{65}{22}\approx2.95$, with $5\cdot\frac{10}{44}=\frac{25}{22}\approx1.14$ left on average.

(The numbers don't quite add up to $10$ because of rounding.)

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