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.
prob of first card black = 13/52
prob of second card also black = 12/51
so prob of 2 black cards
= (13/52)(12/51)
= 1/17
To find the probability of getting two black cards, we need to determine the number of favorable outcomes (getting two black cards) and the total number of possible outcomes (drawing any two cards from the deck).
Step 1: Determine the number of favorable outcomes.
In a standard deck of 52 playing cards, half of the cards are black. So, the first card can be black with a probability of 26/52, or simplified as 1/2.
Once the first card is drawn, there are 51 cards left in the deck, with 25 remaining black cards. Therefore, the second card can be black with a probability of 25/51.
To calculate the probability of both cards being black, we multiply the probabilities of each event occurring: (1/2) * (25/51) = 25/102.
Step 2: Determine the total number of possible outcomes.
When the first card is drawn, there are 52 cards to choose from. When the second card is drawn, only 51 cards remain in the deck.
The total number of possible outcomes is calculated by multiplying the number of options for each draw: 52 * 51 = 2652.
Step 3: Calculate the probability.
Finally, we divide the number of favorable outcomes by the total number of possible outcomes to find the probability:
Probability = Favorable Outcomes / Total Outcomes
Probability = 25/102 / 2652
The answer is a simplified fraction: 25/2652.
To find the probability that both cards are black, we need to determine two factors: the favorable outcomes and the total number of possible outcomes.
1. Favorable outcomes: We want both cards to be black. There are 26 black cards in a standard deck (13 clubs and 13 spades).
2. Total number of possible outcomes: When the first card is dealt, there are 52 cards in the deck. After one card is already drawn, there are 51 cards left for the second draw.
Now, we can calculate the probability:
Probability = (Number of favorable outcomes) / (Total number of possible outcomes)
Number of favorable outcomes = 26 black cards × 25 black cards (since one black card has already been drawn)
= 650
Total number of possible outcomes = 52 × 51
= 2652
Probability = 650 / 2652
To express the answer as a simplified fraction, we can divide the numerator and denominator by their greatest common divisor (GCD):
GCD of 650 and 2652 = 2
650 ÷ 2 = 325, and 2652 ÷ 2 = 1326
Therefore, the simplified fraction is:
Probability = 325 / 1326
Theres 26 black cards in a deck of cards.
Half of the deck of cards will remain red/black.
1/2 of the cards are shown as black cards.