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"In the game of "Between", two cards are dealt and not replaced in the deck. You then pick a third card from the deck. To win, you must pick a card that has a value between the other two cards. The order of values is 2, 3, 4, 5, 6, 7, 8, 9, 10, J, Q, K, A, where the letters represent a jack, queen, king, and ace, respectively. Determine the probability of your winning if the first two cards dealt are the following: a. 5 and a jack b. 2 and a king"

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a. 5/13 b. 10/13
Because in a there are 5 possible options and in b there are 10.
That is what I thought, however when I look it up it is 2/5 and 4/5. I need to show work to complete it.

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Other answers:

hmm, I don't know you you get that, but OK.
given that you're dealt 2 cards, you have 50 left there are 20 cards between 6 and 10 (4 cards for each number) a) 20/50 = 2/5 same concept for b b) 40/50 = 4/5
Oh my gosh! Thank you I have been stuck on that for way too long. It totally makes sense though. I was only thinking of the cards written down.

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