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?
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.
