Answer:
The probability that the two cards drawn form a pair is approximately 0.045.
Step-by-step explanation:
There are 52 cards in an ordinary deck, and each card has a unique rank (ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, jack, queen, or king) and suit (spades, hearts, diamonds, or clubs). There are 13 ranks and 4 suits, so there are 13*4 = 52 possible cards in the deck.
When we draw two cards without replacement, there are 52 ways to draw the first card and 51 ways to draw the second card, for a total of 5251 = 2652 possible outcomes. Of these, there are 4 ways to draw a pair of cards with the same rank (for example, 2 of spades and 2 of hearts) and 13 ranks to choose from, so there are 413 = 52 pairs in the deck. Therefore, the probability of drawing a pair is 52/2652 = 1/51, or approximately 0.0196.
Alternatively, we can calculate the probability by considering the complement of the event (that is, the probability of not drawing a pair). There are 48 non-pair cards in the deck (since there are 52 total cards and 4 pairs), and there are 48*47 = 2256 ways to draw two non-pair cards. Therefore, the probability of not drawing a pair is 2256/2652 = 48/51, or approximately 0.931. The probability of drawing a pair is then 1 - 0.931 = 0.069, or approximately 0.045.
Either way, we can see that the probability of drawing a pair is relatively low, at about 4.5%.