# You are dealt a hand of three cards, one at a time. What is the probability that the first red card you get is the third card dealt?

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Feb 7, 2018

Using the Multiplication rule of probability we get 12.745%

#### Explanation:

Assuming you have a standard deck of 52 cards where one half of the deck is red and one half of the deck is black, you can do this calculation using The Multiplication Rule of Probability. What this law allows us to do is multiply the odds of something happening to get the odds of all the events happening.

Now in order for the first red card to be the third card dealt, the first two cards need to be black. The odds of drawing the first black card are: $\frac{26}{52} = \frac{1}{2}$ and once you draw the black card there are only 25 black cards left and 51 cards in the deck. So the odds of drawing another black card is $\frac{25}{51}$ . Now the deck is down to 50 cards, so the odds of drawing a red card are $\frac{26}{50} = \frac{13}{25.}$

So now we use the multiplication rule and multiply them all together $\frac{1}{2} \cdot \frac{25}{51} \cdot \frac{13}{25}$ which gets you .12745 = 12.745% which is your answer.

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