To determine the probability of drawing 2 spades from 2 standard decks of cards, we first need to consider how many spades are in the decks. Each standard deck has 52 cards, which includes 13 spades. Since we have 2 decks, there are a total of 26 spades available.
The total number of cards in 2 decks is 104 (52 cards per deck times 2). Now, we can calculate the probability step by step:
- For the first draw, the probability of drawing a spade is the number of spades divided by the total number of cards:
P(1st spade) = 26/104 = 1/4. - After drawing one spade, there are now 25 spades left and a total of 103 cards remaining. So, the probability of drawing a second spade becomes:
P(2nd spade) = 25/103.
To find the overall probability of both events happening (drawing 2 spades in succession), we multiply the individual probabilities:
P(2 spades) = P(1st spade) × P(2nd spade) = (26/104) × (25/103) = (1/4) × (25/103) = 25/412.
Therefore, the probability of drawing 2 spades from 2 standard decks of cards is 25/412, or approximately 0.0607, which is about 6.07%.