Suppose that 4 cards are drawn from a well-shuffled deck of 52 cards. What is the probability that all 4 are hearts?
There are 13 hearts of 52 cards.
So, where do I go from here to solve the equation?
The events aren't independent. These kids above are straight up bots
1/52
To find the probability that all 4 cards drawn are hearts, we need to find the ratio of the number of favorable outcomes (all hearts) to the number of possible outcomes (all possible combinations of 4 cards from a deck of 52).
The number of favorable outcomes would be the number of ways to choose all 4 hearts from the 13 hearts available.
The number of possible outcomes would be the number of ways to choose any 4 cards from the 52 cards in the deck.
To calculate this, we need to use the concept of combinations. The number of combinations of k items chosen from a set of n items is denoted as nCk or "n choose k" and is calculated as n! / (k!(n-k)!), where ! represents the factorial of a number.
In this case, we have n = 52 (total number of cards) and k = 4 (number of hearts). So, the number of ways to choose all 4 hearts from the deck would be 13C4, calculated as:
13! / (4!(13-4)!) = 13! / (4!9!)
To continue solving this, you can simplify the factorials in the numerator and denominator and then calculate the value of 13! / (4!9!).
Once you have this value, the probability can be found by dividing the number of favorable outcomes by the number of possible outcomes.
If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.
13/52 * 12/51 * 11/50 * 10/49 = ?