Two cards are selected at random without replacement from a well-shuffled deck of 52 playing cards. Find the probability of the given event. A pair is not drawn.

since there is no restriction on the first card, p(pair) = p(2nd card is same value as 1st card)

p(pair) = 1 * 3/51 = 1/17

p(no pair) = 16/17

To find the probability of not drawing a pair, we first need to find the total number of possible outcomes.

When two cards are drawn at random without replacement from a deck of 52 cards, the first card can be any of the 52 cards, and the second card can be any of the remaining 51 cards.

Therefore, the total number of possible outcomes is 52 * 51 = 2,652.

Now, let's determine the number of favorable outcomes, i.e., the number of ways to not draw a pair.

For the first card, we have 52 options. For the second card, there are 3 possibilities to avoid getting a pair. If the first card is, for example, the Ace of Spades, the second card must not be either of the other two Aces (Ace of Hearts or Ace of Diamonds). Similarly, if the first card is the King of Clubs, the second card must not be either of the other three Kings, and so on.

Therefore, the number of favorable outcomes is 52 * 3 = 156.

The probability of not drawing a pair is given by the number of favorable outcomes divided by the total number of possible outcomes:

P(not drawing a pair) = favorable outcomes / total outcomes
= 156 / 2,652
≈ 0.0587

So, the probability of not drawing a pair is approximately 0.0587, or 5.87%.

To find the probability of not drawing a pair when selecting two cards without replacement from a deck of 52 playing cards, we first need to determine the total number of possible outcomes and the number of favorable outcomes.

Total Number of Possible Outcomes:
When two cards are selected without replacement, the first card can be any of the 52 cards in the deck. After removing one card, the second card can be any of the remaining 51 cards. Therefore, the total number of possible outcomes is 52 * 51 = 2,652.

Number of Favorable Outcomes (Not drawing a pair):
To not draw a pair, we need to make sure that the two selected cards have different ranks. The first card can be any of the 52 cards in the deck. For the second card, there are 3 cards of the same rank as the first card (since there are 4 cards of each rank), and the remaining cards can be any of the 51 remaining cards. Therefore, the number of favorable outcomes is 52 * 3 * 51 = 7,884.

Probability:
The probability of an event is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.

P(not drawing a pair) = Number of Favorable Outcomes / Total Number of Possible Outcomes
= 7,884 / 2,652
≈ 0.297

Therefore, the probability of not drawing a pair when selecting two cards without replacement from a well-shuffled deck of 52 playing cards is approximately 0.297, or 29.7%.