If you are dealt 2 cards from a standard deck of 52 cards what is the probability that they will both be aces? Give answers as decimal to 5 decimal places not percent.
4C2 ways to get two aces
52C2 ways to get two cards
4C2 / 52C2 = ?
To determine the probability of getting both aces when dealt 2 cards from a standard deck of 52 cards, we need to find the ratio of successful outcomes to total possible outcomes.
Step 1: Find the number of successful outcomes.
In a standard deck of 52 cards, there are 4 aces. We need to find the number of ways we can get 2 aces from these 4 aces. This can be calculated using combinations - "nCr" notation. The number of ways to choose 2 aces from 4 is written as 4C2, which is equal to (4!)/(2!(4-2)!). Evaluating this expression gives us 6.
So, there are 6 different combinations in which we can select 2 aces from a standard deck of 52 cards.
Step 2: Find the total number of possible outcomes.
When dealing 2 cards from a standard deck of 52 cards, the total number of possible outcomes can be calculated using combinations as well. This time, we want to choose 2 cards from the entire deck, so the total number of ways to do this is 52C2, which is equal to (52!)/(2!(52-2)!). Evaluating this expression gives us 1326.
So, there are 1326 different combinations when 2 cards are dealt from a standard deck of 52 cards.
Step 3: Calculate the probability.
To find the probability, we divide the number of successful outcomes (6) by the total number of possible outcomes (1326).
Probability = Successful outcomes / Total outcomes
Probability = 6 / 1326
Probability ≈ 0.00453 (rounded to 5 decimal places)
Therefore, the probability of getting both aces when dealt 2 cards from a standard deck of 52 cards is approximately 0.00453.