Two cards are drawn with replacement from an ordinary deck of 52 playing cards. What is the probability that the first card is a heart and the second card is a diamond?
To find the probability of drawing a heart on the first card and a diamond on the second card, we need to consider the number of favorable outcomes and the total number of possible outcomes.
Step 1: Find the probability of drawing a heart on the first card.
There are 13 hearts in a deck of 52 cards, so the probability of drawing a heart on the first card is 13/52.
Step 2: Find the probability of drawing a diamond on the second card.
Likewise, there are 13 diamonds in a deck of 52 cards, so the probability of drawing a diamond on the second card is also 13/52.
Step 3: Calculate the combined probability.
Since the two events are independent (as the cards are drawn with replacement), we can calculate the combined probability by multiplying the individual probabilities:
Probability = (13/52) * (13/52)
= (169/2704)
= 0.0625
So, the probability of drawing a heart on the first card and a diamond on the second card is 0.0625 or 6.25%.
To find the probability that the first card is a heart and the second card is a diamond, we need to determine the number of favorable outcomes and the total number of possible outcomes.
First, let's calculate the number of favorable outcomes:
1. The probability of drawing a heart as the first card is 13 hearts out of 52 cards since there are 13 hearts in a deck.
2. After replacing the first card back into the deck, the probability of drawing a diamond as the second card is also 13 diamonds out of 52 cards.
To calculate the total number of possible outcomes:
Since each card is being replaced after being drawn, the total number of possible outcomes remains at 52 cards for each draw.
Now we can calculate the probability:
The probability of the first card being a heart and the second card being a diamond is calculated by multiplying the probabilities of each event together.
P(first card is a heart and second card is a diamond) = P(first card is a heart) * P(second card is a diamond)
= (13/52) * (13/52)
= (1/4) * (1/4)
= 1/16
Therefore, the probability that the first card is a heart and the second card is a diamond is 1/16 or approximately 0.0625.
13/52*13/51
Um, possible typo there?
If the cards are drawn _with_ replacement, the first card is back in the deck when the second is drawn, and the probability of the second being a diamond is again 13/52?