The probability that the next card picked is the four of diamonds?

Mathematics
Tutor: None Selected Time limit: 1 Day

During a game of Gin Rummy, Sven needs the four of diamonds to make a straight in his hand. He and the other player have been dealt 10 cards each, the other player does not have the card he wants, and all other cards are in the deck. What is the probability that the next card picked from the deck is the four of diamonds? Express your answer as an integer or a simplified fraction.

May 29th, 2015

There are 52 cards in a standard deck. If 20 were dealt out between the two players, then there's only 32 left in the deck.

The probability that the four of diamonds is in the deck is 100 percent (unless one of the cards is a joker and the four of diamonds is really missing ;) you never know.). But the probability that the next card is a four of diamonds is kind of a two part question. Because it's not only asking what the probability of drawing the four of diamonds is, but that you draw it.

It would be like asking the probability of drawing the four of diamonds on exactly the third draw or the fifth or any one. This means that you are multiplying the probability of drawing anything else by however many cards until you draw the one you want, then you multiply it by the probability of drawing that card.

So in this case, the probability of drawing that card first doesn't affect anything. It means the same as just drawing the card at all, and that probability is 1 (cause there's only 1 four of diamonds in a deck of cards) out of 32 (the number of cards there are).

So the fraction is 1/32.

Let me know if you have any questions and if I can help you with anything in the future. 

Take care partner.

-Doctor Turner 

May 29th, 2015

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May 29th, 2015
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