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.)
A pair is not drawn.
well, after you draw a card (any card), there are 48 of the remaining 51 which do not match it, right?
To find the probability of not drawing a pair, 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 drawn 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. So, the total number of possible outcomes is 52 * 51 = 2,652.
Number of favorable outcomes:
To not draw a pair, we need to select two cards that are of different ranks and different suits.
For the first card, we have 52 options.
For the second card, we have 3 possibilities for its rank (since it cannot be the same rank as the first card) and 4 possibilities for its suit (since it cannot be the same suit as the first card).
So, the number of favorable outcomes is 52 * 3 * 4 = 624.
Probability of not drawing a pair:
Probability 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
P(not drawing a pair) = 624 / 2652 ≈ 0.235
Therefore, the probability of not drawing a pair is approximately 0.235, rounded to three decimal places.