Question

You randomly draw two cards from a standard deck of 52 playing cards. What's the probability of drawing two black cards? With replacement Without replacement

Answer 1

The probability of drawing two black cards is 1/4 or 0.25 with replacement and 25/102 or approximately 0.245 without replacement from a standard deck of 52 playing cards.

Step-by-step explanation:

To find the probability of drawing two black cards, we need to consider the number of black cards and the total number of cards in the deck. A standard deck of 52 playing cards has 26 black cards (clubs and spades) and 52 cards in total.

With replacement:

When drawing with replacement, each card is replaced after it is drawn, so the number of black cards and the total number of cards remain the same for the second draw. The probability of drawing a black card on the first draw is 26/52 = 1/2. And since each draw is independent, the probability of drawing a black card on the second draw is also 1/2. Therefore, the probability of drawing two black cards with replacement is (1/2) * (1/2) = 1/4 or 0.25.

Without replacement:

When drawing without replacement, the deck changes after each draw because the cards are not replaced. The probability of drawing a black card on the first draw is still 26/52 = 1/2. However, on the second draw, there are now only 25 black cards left out of 51 total cards. So the probability of drawing a black card on the second draw decreases to 25/51. Therefore, the probability of drawing two black cards without replacement is (1/2) * (25/51) = 25/102 or approximately 0.245.

Answer 2

The probability of drawing two black cards is 25% with replacement and 24.5% without replacement.

Probability of drawing two black cards:

With replacement:

Total outcomes: The total number of possible outcomes for drawing two cards is 52 * 52 = 2704.

The probability of drawing two black cards with replacement is the number of favorable outcomes divided by the total number of outcomes, which is 676 / 2704 = 0.25 or 25%

Without replacement:

The total number of possible outcomes for drawing two cards without replacement is 52 * 51 = 2652.

The probability of drawing two black cards without replacement is 650 / 2652 = 0.245 or 24.5%

Therefore, the probability of drawing two black cards is 25% with replacement and 24.5% without replacement.