Four cards are chosen at random. What is the probability that at least 2 are J's? How is this problem computed? Using Combinations or permutations?
Since the order of choice is not important, you would use combinations.
To compute the probability that at least 2 out of 4 chosen cards are J's, we need to consider the different cases where exactly 2, 3, or 4 J's are selected.
To calculate this probability, we can use combinations.
First, we need to determine the total number of possible outcomes. Since we are choosing 4 cards at random from a deck, there are 52 cards to choose from, and we need to select 4 cards. So the total number of possible outcomes is given by the combination formula:
C(n, r) = n! / (r! * (n - r)!)
In this case, n = 52 (total number of cards) and r = 4 (number of cards chosen).
Next, we calculate the number of favorable outcomes, i.e., the number of ways to choose at least 2 J's from the deck.
Case 1: Exactly 2 J's:
The number of ways to select 2 J's from 4 J's available is C(4, 2).
Case 2: Exactly 3 J's:
The number of ways to select 3 J's from 4 J's available is C(4, 3).
Case 3: All 4 J's:
There is only 1 way to select all 4 J's.
Now, we can calculate the total number of favorable outcomes by summing up the results from each case:
Total favorable outcomes = C(4, 2) + C(4, 3) + 1
Finally, we divide the total favorable outcomes by the total possible outcomes to obtain the probability:
Probability = Total favorable outcomes / Total possible outcomes
Note: In this problem, we assume that the deck is well-shuffled and does not contain any duplicates.
Using this approach and the combination formula, we can compute the probability that at least 2 out of 4 selected cards are J's.