what is the probability of drawing a diamond face card on the fifth draw from a standard deck of 52 cards, knowing that the first four draws removed four kings from the deck
Since the four kings have been drawn, only 48 cards and 12 diamonds remain.
P = 12/48 = 1/4 = .25
To calculate the probability of drawing a diamond face card on the fifth draw after removing four kings from a standard deck of 52 cards, we need to determine the number of favorable outcomes (diamond face cards) and the number of possible outcomes (remaining cards in the deck).
Step 1: Determine the number of favorable outcomes:
In a standard deck of 52 cards, there are 3 face cards (jack, queen, and king) for each of the 4 suits (hearts, diamonds, clubs, and spades), making a total of 3 * 4 = 12 face cards. Since we have already removed 4 kings from the deck, the number of favorable outcomes (diamond face cards remaining) is 3.
Step 2: Determine the number of possible outcomes:
After removing 4 kings from the deck, there are 52 - 4 = 48 cards remaining.
Step 3: Calculate the probability:
The probability of drawing a diamond face card on the fifth draw is calculated by dividing the number of favorable outcomes by the number of possible outcomes:
Probability = Favorable outcomes / Possible outcomes
= 3 / 48
= 1 / 16
Therefore, the probability of drawing a diamond face card on the fifth draw, given that the first four draws removed four kings, is 1/16.
To find the probability of drawing a diamond face card on the fifth draw from a standard deck of 52 cards, knowing that the first four draws removed four kings, we can follow these steps:
Step 1: Determine the number of diamond face cards remaining in the deck.
In a standard deck of 52 cards, there are 13 diamonds. Since there are 3 face cards in each suit (namely jack, queen, and king), there are a total of 3 * 13 = 39 face cards. However, since we've removed four kings, there are now 39 - 4 = 35 face cards remaining.
Step 2: Determine the number of cards remaining in the deck.
After removing four kings from the deck, there are 52 - 4 = 48 cards remaining.
Step 3: Determine the number of favorable outcomes.
The favorable outcome in this case is drawing a diamond face card. Since there are 13 diamonds in the deck and 3 face cards in the suit, there are 13 * 3 = 39 favorable outcomes.
Step 4: Determine the total number of possible outcomes.
The total number of possible outcomes is the number of cards remaining in the deck, which is 48.
Step 5: Calculate the probability.
The probability of drawing a diamond face card on the fifth draw is determined by dividing the number of favorable outcomes by the total number of possible outcomes:
Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = 39 / 48 ≈ 0.8125
So, the probability of drawing a diamond face card on the fifth draw, given that the first four draws removed four kings, is approximately 0.8125 or 81.25%.