You are dealt two cards successively without replacement from a standard deck of 52 playing cards. Find the probability that both cards are black.
# of black cards/total cards * number of remaining black cards/remaining total cards.
This is an "and" relationship.
So if there are 26 black cards in a deck you would take 26/52*24/50 right??
you probability of picking the first card is right, but (since one black card has already been picked without replacement) the probability of picking the second black card is 25/51.
To find the probability that both cards are black, we need to determine the number of favorable outcomes and divide it by the total number of possible outcomes.
Let's break it down step by step:
Step 1: Determine the number of favorable outcomes.
In a standard deck of 52 playing cards, half of them are black. There are 26 black cards (clubs and spades) in the deck. Since we are drawing two cards successively without replacement, the number of favorable outcomes for the first card would be 26 (all the black cards in the deck). After drawing the first black card, there will be 25 black cards left in the deck. Therefore, the number of favorable outcomes for the second card would be 25 black cards.
So, the number of favorable outcomes is 26 * 25 = 650.
Step 2: Determine the total number of possible outcomes.
When we draw the first card, there are 52 cards in the deck, and when we draw the second card, there are 51 cards left in the deck. So, the total number of possible outcomes is 52 * 51 = 2,652.
Step 3: Calculate the probability.
The probability of an event occurring is given by the formula:
Probability = (Number of Favorable Outcomes) / (Total Number of Possible Outcomes).
In this case, the probability of drawing two black cards successively without replacement is:
Probability = 650 / 2,652 ≈ 0.245 or 24.5%.
Therefore, the probability that both cards are black is approximately 24.5%.