So the other day I took a math test, (not for class, its just an optional test, so this isn't and kind of cheating) which included all kinds of logical and problem solving exercises, among others this one:
-"Given a deck of cards with N cards in it and each card is numbered (so the cards are 1, 2, 3, 4, … nth card). Two cards are drawn one after each other. What is the probability that the when a third card is drawn, that this third cards number is in between the first card's and the second card's number."
I had done most of this test without problems but I just couldn't get around the fact that N (the number of cards) is unknown, so I'm not sure if the result should be a function of N or whether its an independent number.
Any kind of help is greatly appreciated!
I can post some more of the questions if anyone is willing to see, the exam is something a teacher does for those students who want to stay after school and test out their logical and problem solving skills
Best Answer
The answer is $\frac13$.
There are six different ways the top three cards can be arranged. Two of those arrangements have the middle valued card in the third spot from the top.