you are dealt two cards successively(without Placement)from a shuffled deck of 52 playing cards .find the probability that both cards are black .express your answer as a simplified fraction.

(26/52)*(25/51)

To find the probability that both cards are black, we need to calculate the number of favorable outcomes (in this case, the number of ways to draw two black cards) divided by the total number of possible outcomes (the number of ways to draw any two cards from a shuffled deck of 52 cards).

Step 1: Calculate the number of ways to draw two black cards.
The number of ways to draw the first black card is 26 (since there are 26 black cards in a deck of 52 cards).
After drawing the first black card, there are 25 black cards left out of the remaining 51 cards, so the number of ways to draw the second black card is 25.
Therefore, the number of favorable outcomes is 26 * 25 = 650.

Step 2: Calculate the total number of possible outcomes.
The total number of ways to draw any two cards from a shuffled deck of 52 cards is given by the combination formula: C(52, 2) = 52! / (2! * (52-2)!) = 1326.

Step 3: Calculate the probability.
The probability is given by the number of favorable outcomes divided by the total number of possible outcomes.
P(both cards are black) = 650 / 1326.

Step 4: Simplify the fraction.
To simplify the fraction, we can divide both the numerator and denominator by their greatest common divisor (GCD).
The GCD of 650 and 1326 is 2.
P(both cards are black) = (650/2) / (1326/2) = 325 / 663.

Therefore, the probability that both cards drawn successively without replacement are black is 325/663.

To find the probability that both cards are black, we need to determine the number of favorable outcomes (black cards) and the total number of possible outcomes.

1. Number of favorable outcomes:
There are 26 black cards in a standard deck of 52 playing cards. When the first card is dealt, there are still 25 black cards left in the deck. Therefore, the number of favorable outcomes is 26 (for the first black card) multiplied by 25 (for the second black card), which gives us a total of 650 favorable outcomes.

2. Total number of possible outcomes:
When the first card is dealt, there are 52 cards in the deck. For the second card, there are 51 cards remaining. Thus, the total number of possible outcomes is 52 multiplied by 51, resulting in 2,652 possible outcomes.

3. Calculating the probability:
The probability is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.

Probability = Number of favorable outcomes / Total number of possible outcomes

Probability = 650 / 2,652

Now, let's simplify this fraction. To do so, we can divide both the numerator and denominator by their greatest common divisor, which is 2 in this case.

Probability = (650 ÷ 2) / (2,652 ÷ 2)

Simplifying further:

Probability = 325 / 1,326

Therefore, the probability that both cards dealt successively are black is 325/1326.