Two cards are selected at random without replacement from a well-shuffled deck of 52 playing cards. Find the probability of the given event. (Round your answer to three decimal places.)

find the probability that A pair is not drawn.

To find the probability that a pair is not drawn, we need to calculate the probability of selecting two cards that are not of the same rank.

First, let's determine the total number of ways to select two cards out of a deck of 52 cards without replacement.

The number of ways to choose the first card is 52 (since any of the 52 cards can be chosen first). Then, there are 51 cards left in the deck, so the number of ways to choose the second card is 51. Therefore, the total number of ways to choose two cards is 52 * 51 = 2,652.

Next, let's determine the number of ways to select two cards that are not of the same rank.

Each rank in the deck has four cards, one from each suit (hearts, diamonds, clubs, and spades). So, for the first card, we can choose any of the 52 cards. However, for the second card, we cannot choose a card of the same rank, which leaves us with three cards of each rank (out of the four suits) that we can select from. Therefore, the number of ways to select two cards that are not of the same rank is 52 * 3 = 156.

Finally, we can calculate the probability by dividing the number of favorable outcomes (selecting two cards that are not of the same rank) by the total number of possible outcomes (selecting any two cards):

Probability = Number of favorable outcomes / Total number of possible outcomes
= 156 / 2,652
≈ 0.059

Therefore, the probability that a pair is not drawn is approximately 0.059 (rounded to three decimal places).

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