There are 52 cards in a standard deck of cards. You shuffle the deck and pull out a card, replace it, and pull another card. What is the probability you pull out an ace and then pull out the 3 hearts??
There are 4 aces in a deck of cards, and there is 1 ace of hearts in those 4 aces. Therefore, the probability of pulling out an ace is 1/13.
Once you have pulled out the ace, there are 13 hearts in a deck, and only 1 of them is a 3. Therefore, the probability of pulling out the 3 of hearts is 1/13.
To find the probability of both events happening, you multiply the probabilities together:
(1/13) * (1/13) = 1/169
Therefore, the probability of pulling out an ace and then pulling out the 3 of hearts is 1/169.
Is this an most likely or no
The probability of pulling out an ace and then pulling out the 3 of hearts is 1/169, which is a relatively low probability. This means that it is not very likely that you will pull out an ace and then pull out the 3 of hearts when shuffling and drawing cards from a standard deck.
So this goes with the question I asked at first, What is the likelihood of selecting an Ace, replacing it, and then selecting a 3 of Hearts? (Hint: Look at the answer of 0.1%)
I apologize for the mistake in my previous responses. Let's reevaluate the probability of selecting an Ace, replacing it, and then selecting the 3 of Hearts from a standard deck of cards.
The probability of selecting an Ace from a standard deck of 52 cards is 4/52 = 1/13.
Since the Ace is replaced before the next draw, the deck is back to its original composition, and the probability of selecting the 3 of Hearts is 1/52.
To find the overall probability of selecting an Ace and then selecting the 3 of Hearts, we multiply the individual probabilities:
(1/13) * (1/52) = 1/676
Therefore, the likelihood of selecting an Ace, replacing it, and then selecting the 3 of Hearts from a standard deck of cards is 1/676, which is approximately 0.148% or approximately 0.1%.