5 cards are drawn at random from a standard deck of playing cards. What is the probability that all are the same suit?
Assuming no replacement, each time there is one less card in each category.
13/52 * 12/51 * 11/50 * 10/49 * 9/48 = ?
Gabe is doing a probability experiment. He is tossing a coin and spinning a spinner with 4 equal sections labeled 1 through 4. How many possible outcomes are there
To calculate the probability of drawing 5 cards of the same suit from a standard deck of playing cards, we need to determine the total number of favorable outcomes (drawing 5 cards of the same suit) and the total number of possible outcomes (drawing any 5 cards from the deck).
First, let's find the number of favorable outcomes. There are four different suits in a deck of cards (hearts, diamonds, clubs, and spades). For each suit, there are 13 cards (Ace through King). So, we have 13 favorable outcomes for each suit, resulting in a total of 4 * 13 = 52 favorable outcomes (since there are 4 suits).
Next, let's find the total number of possible outcomes. We are drawing 5 cards from a deck of 52 cards, which can be accomplished in C(52, 5) ways. Using the concept of combinations, we can calculate this as:
C(n, r) = n! / (r! * (n - r)!)
C(52, 5) = 52! / (5! * (52 - 5)!)
Simplifying this expression, we get:
C(52, 5) = 52! / (5! * 47!)
Now, let's calculate this value:
C(52, 5) = (52 * 51 * 50 * 49 * 48) / (5 * 4 * 3 * 2 * 1)
= 2,598,960
Therefore, there are 2,598,960 possible outcomes when drawing any 5 cards from a standard deck.
Now, we can calculate the probability by dividing the number of favorable outcomes by the number of possible outcomes:
Probability = Favorable outcomes / Possible outcomes
= 52 / 2,598,960
≈ 0.00002
So, the probability of drawing 5 cards of the same suit from a standard deck is approximately 0.00002, or 0.002%.