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A deck of cards has 20 cards,  red cards numbered 1-10 and  blue cards numbered 1-10

Suppose we shuffle the deck and draw the top two cards. What is the probability that they have the same number?

 May 6, 2023
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The probability that the two cards have the same number is 10/19​.

There are 20 cards in the deck, 10 red cards numbered 1-10 and 10 blue cards numbered 1-10. The probability of drawing a red card is 10/20=1/2​. The probability of drawing a blue card is also 1/2​.

If the first card is red, the probability that the second card is also red is 9/19. If the first card is blue, the probability that the second card is also blue is 9/19​.

Therefore, the probability that the two cards have the same number is 1/2*9/19 + 1/2*9/19 = 10/19.

 May 6, 2023

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