SOLUTION: Hello everyone! I'm a fellow tutor that is preparing a student on his homework and I came across this problem and it is really stumping me: "Consider a normal deck of playing c

Question 1140962: Hello everyone! I'm a fellow tutor that is preparing a student on his homework and I came across this problem and it is really stumping me:
"Consider a normal deck of playing cards. You and your friend decide to play Go Fish. You deal out 5 cards to your friend and 5 to yourself. You have all face cards (jack, queen, king). Your friend shouts 'All my cards are red!'. Given that information what is the probability your friend has a face card?"
I know that the solution involves using combinations rather than permutations, but beyond that this is really confusing as to how to approach it. Can anyone help me with this? Thanks in advance!!
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
The friend's sample space is 26 red cards with 5 chosen or 26C5
If we look at the probability he was dealt no face cards, that would mean 20C5.
20C5/26C5 is 0.2357 so the probability he was dealt at least one face card is the complement of that, or 0.7643.

It is possible to look at what the dealer had, but the dealer came second.

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