4 cards drawn at random find probability all cards are hearts
There are 52 cards in a deck, 13 of which are hearts.
The probability of drawing a heart on the first card is 13/52.
After drawing a heart, there are only 51 cards left in the deck, 12 of which are hearts.
The probability of drawing another heart on the second card is 12/51.
After drawing two hearts, there are only 50 cards left in the deck, 11 of which are hearts.
The probability of drawing a third heart is 11/50.
After drawing three hearts, there are only 49 cards left in the deck, 10 of which are hearts.
The probability of drawing a fourth heart is 10/49.
To find the probability of all four cards being hearts, we multiply the probabilities of each individual event:
(13/52) x (12/51) x (11/50) x (10/49) = 0.0026 or 0.26%.
Therefore, the probability of drawing all four cards as hearts is approximately 0.26%.
Find the probability all face cards
4 cards drawn at random find probability all cards are face cards
To find the probability that all four cards drawn are hearts, we need to know the total number of possible outcomes and the number of favorable outcomes.
Step 1: Determine the total number of possible outcomes.
In a standard deck of 52 playing cards, there are a total of 52 cards. Since we are drawing four cards without replacement, the total number of possible outcomes can be calculated using the concept of combinations. The number of combinations of 52 cards taken 4 at a time is denoted as C(52, 4) and can be calculated as follows:
C(52, 4) = 52! / (4! * (52 - 4)!) = 52! / (4! * 48!) = (52 * 51 * 50 * 49) / (4 * 3 * 2 * 1) = 270,725
So, there are a total of 270,725 possible outcomes.
Step 2: Determine the number of favorable outcomes.
In a standard deck of 52 playing cards, there are 13 hearts. Since we want to draw all four cards as hearts, the number of favorable outcomes is simply the number of combinations of 13 hearts taken 4 at a time, denoted as C(13, 4):
C(13, 4) = 13! / (4! * (13 - 4)!) = 13! / (4! * 9!) = (13 * 12 * 11 * 10) / (4 * 3 * 2 * 1) = 715
So, there are a total of 715 favorable outcomes.
Step 3: Calculate the probability.
To find the probability that all four cards drawn are hearts, we divide the number of favorable outcomes by the total number of possible outcomes:
Probability = Favorable Outcomes / Total Outcomes
Probability = 715 / 270,725
Probability ≈ 0.00264 (rounded to 5 decimal places)
Therefore, the probability that all four cards drawn are hearts is approximately 0.00264 or 0.264%.