A standard deck of cards contains 52 cards. Of these cards there are 13 of each type of suit (hearts, spades, clubs, diamonds) and 4 of each type of rank (A – K). Two cards are drawn from the deck and replaced each time back into the deck. What is the probability of drawing the King of Clubs and a heart from the deck of cards?
1/52 * 1/4
What is the probability of spinning a white section or a number less than 3?
To find the probability of drawing the King of Clubs and a heart from the deck of cards, we need to determine the probability of drawing the King of Clubs on the first draw and a heart on the second draw.
Step 1: Find the probability of drawing the King of Clubs on the first draw.
There is 1 King of Clubs out of 52 cards in the deck. So, the probability of drawing the King of Clubs on the first draw is 1/52.
Step 2: Find the probability of drawing a heart on the second draw.
After replacing the first card back into the deck, there are now 52 cards remaining. Out of these, there are 13 hearts. So, the probability of drawing a heart on the second draw is 13/52.
Step 3: Multiply the probabilities from steps 1 and 2.
To find the combined probability, we multiply the probabilities from step 1 and step 2: (1/52) * (13/52) = 13/2704.
So, the probability of drawing the King of Clubs and a heart from the deck of cards is 13/2704.
To calculate the probability of drawing the King of Clubs and a heart from the deck of cards, we need to determine the total number of possible outcomes and the number of favorable outcomes.
First, let's calculate the total number of possible outcomes. Since two cards are drawn with replacement each time, the total number of outcomes for each draw is equal to the total number of cards in the deck. In this case, there are 52 cards, so for each draw, there are 52 possible outcomes.
Next, let's calculate the number of favorable outcomes. We want to draw the King of Clubs and a heart. There is only one King of Clubs in the deck and there are 13 hearts. Since the two draws are independent (with replacement), the probability of drawing the King of Clubs and a heart is equal to the product of their individual probabilities.
The probability of drawing the King of Clubs is 1/52, as there is only one King of Clubs out of 52 cards.
The probability of drawing a heart is 13/52, as there are 13 hearts out of 52 cards.
Now, we can calculate the probability of drawing both the King of Clubs and a heart by multiplying their individual probabilities:
Probability = (1/52) * (13/52) = 1/202
Therefore, the probability of drawing the King of Clubs and a heart from the deck of cards is 1/202.