There are 52 playing cards in a standard deck of cards. If Patrica selects a card at random, what is the probability that it will be a black queen then a red card without replacing the first card.

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28-04-2017
Mathematics

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There are 52 playing cards in a standard deck of cards. If Patrica selects a card at random, what is the probability that it will be a black queen then a red card without replacing the first card.

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BackPacker99 BackPacker99 · Answer 1 · 2017-04-28T04:26:20+02:00

Since there are two black queens out of 52 cards, there is a 2/52 chance of drawing a black queen first. This is equivalent to a 1/26 chance.

Now that we have removed a black queen, there are 51 cards left in the deck. 26 of them are red because we only took away a black card. This means that there is a 26/51 of drawing a red card next.

In order to find the probability of both of these happening, we multiply the two together. 1/26 * 26/51 = 26/1326. This reduces to 1/51. So, there is a 1/51 chance of drawing a black queen, then a red card.