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A standard deck of cards has 52 cards divided into 4 suits, each of which has 13 cards. Two of the suits ($\heartsuit$ and $\diamondsuit$, called `hearts' and `diamonds') are red, the other two ($\spadesuit$ and $\clubsuit$, called `spades' and `clubs') are black. The cards in the deck are placed in random order (usually by a process called `shuffling'). What is the probability that the first two cards drawn from the deck are both red?

 Mar 29, 2021
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Hey there!

 

From your definitions we know that there are 26 red cards in the deck. I'm assuming that there is no replacement when the first card is drawn. The chance of you drawing a red card first is \(\frac{26}{52}\) then, since a red card is removed from the deck, the chance of getting a second red card is \(\frac{25}{51}\). We then multiply this together to get the probability of this occurring:

 

\(\frac{26}{52}\times \frac{25}{51} \approx 0.2451 \approx 24.51\%\)

 

Hope this helped :)

 Mar 29, 2021

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