Three cards are drawn without replacement from a well-shuffled deck of 52 playing cards. What is the probability that the third card drawn is a diamond?
To find the probability that the third card drawn is a diamond, we need to determine the total number of possible outcomes and the number of favorable outcomes.
Step 1: Total number of possible outcomes
When drawing three cards without replacement from a deck of 52 playing cards, the total number of possible outcomes can be calculated using the concept of combinations. The number of ways to choose 3 cards out of 52 is given by the combination formula:
C(52, 3) = 52! / (3! * (52-3)!) = 22,100
So, there are 22,100 possible outcomes when drawing three cards from the deck.
Step 2: Number of favorable outcomes
To calculate the number of favorable outcomes, we need to consider the number of diamonds remaining in the deck after the first two cards are drawn.
In a standard deck of 52 cards, there are 13 diamonds. When the first card is drawn, there are still 13 diamonds and 51 remaining cards. After the second card is drawn, there are 12 diamonds and 50 remaining cards. Finally, when the third card is drawn, there are 11 diamonds and 49 remaining cards.
So, the number of favorable outcomes is 11.
Step 3: Calculate the probability
Now that we have the number of favorable outcomes and the total number of possible outcomes, we can calculate the probability:
Probability = Favorable outcomes / Total outcomes
Probability = 11 / 22,100 ≈ 0.0004986
Therefore, the probability that the third card drawn is a diamond is approximately 0.0004986 or 0.04986%.