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 pulled in order, without replacement from this deck of 52 playing cards. What is the probability that the cards will be an 8 of hearts and then an Ace?
You want the 8 of hearts, then an Ace
prob = (1/52)(4/51) = 1/663
Well, the probability of pulling the 8 of hearts as the first card is 1 out of 52, since there is only one 8 of hearts in the deck.
Then, after you've pulled the first card, there are 51 cards left in the deck, and there is now only one Ace remaining. So, the probability of pulling the Ace as the second card is 1 out of 51.
To find the probability of both events happening, we multiply the individual probabilities.
So, the probability of pulling an 8 of hearts and then an Ace is (1/52) * (1/51) = 1/2652.
But hey, don't feel too bad if you don't get that exact combination – there are plenty of other card tricks you can try!
To find the probability of drawing an 8 of hearts and then an Ace, we need to determine the number of favorable outcomes and the total number of possible outcomes.
Step 1: Determine the number of favorable outcomes.
Since there are only one 8 of hearts and one Ace in the deck, there is only one favorable outcome.
Number of favorable outcomes = 1
Step 2: Determine the total number of possible outcomes.
When the first card is drawn, there are 52 cards remaining in the deck.
When the second card is drawn, there are 51 cards remaining in the deck.
Total number of possible outcomes = 52 * 51 = 2652
Step 3: Calculate the probability.
The probability is defined as the number of favorable outcomes divided by the total number of possible outcomes.
Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = 1 / 2652
Therefore, the probability of drawing an 8 of hearts and then an Ace is 1/2652.
To find the probability of the event, we need to divide the number of favorable outcomes (getting an 8 of hearts followed by an Ace) by the total number of possible outcomes.
Step 1: Find the number of favorable outcomes:
There is only one 8 of hearts in the deck and only one Ace. Therefore, the number of favorable outcomes is 1.
Step 2: Find the total number of possible outcomes:
We are selecting 2 cards without replacement from a deck of 52 cards. Initially, there are 52 possibilities for the first card. After selecting the first card, there are only 51 cards left for the second selection. Therefore, the total number of possible outcomes is 52 * 51.
Step 3: Calculate the probability:
Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = 1 / (52 * 51)
Probability = 1 / 2652
So, the probability of pulling an 8 of hearts and then an Ace is 1/2652.