Find the probability of drawing the face card that is a spade on the first-draw replacing it and drawing a king card on the second draw
To find the probability of drawing a face card that is a spade on the first draw, replacing it, and then drawing a king card on the second draw, we need to consider the total number of possible outcomes and the desired outcomes.
Let's break down the problem step by step:
Step 1: Finding the probability of drawing a face card that is a spade on the first draw.
- A standard deck of cards has 52 cards.
- Out of these 52 cards, there are 13 spades, and since each suit has 3 face cards (jack, queen, and king), there are a total of 12 face cards that are spades.
- Therefore, the probability of drawing a face card that is a spade on the first draw is 12/52.
Step 2: Replacing the card after the first draw (assuming it is put back into the deck).
- By replacing the card, we reset the deck back to 52 cards, meaning each card has an equal probability of being drawn again. Therefore, the probability remains the same as in Step 1: 12/52.
Step 3: Finding the probability of drawing a king card on the second draw.
- After the first draw, we have put the card back into the deck, so there are still 52 cards in total.
- Out of these 52 cards, there are 4 kings in the deck (one for each suit).
- Therefore, the probability of drawing a king card on the second draw is 4/52.
Step 4: Combining the probabilities.
- To find the overall probability of both events happening (drawing a face card that is a spade on the first draw and then drawing a king card on the second draw), we multiply the probabilities from Steps 1, 2, and 3:
(12/52) * (12/52) * (4/52) = 0.0146
So, the probability of drawing a face card that is a spade on the first draw, replacing it, and then drawing a king card on the second draw is approximately 0.0146, or 1.46%.
To find the probability of drawing a face card that is a spade on the first draw and a king card on the second draw (replacing the first card), we need to consider the number of favorable outcomes and the total number of possible outcomes.
Step 1: Determine the number of favorable outcomes:
There are 3 face cards that are spades in a deck of 52 cards (Ace of Spades, King of Spades, and Queen of Spades). So, the number of favorable outcomes is 3.
Step 2: Determine the total number of possible outcomes:
A standard deck of cards has 52 cards, so the total number of possible outcomes is 52.
Step 3: Calculate the probability:
To find the probability, we divide the number of favorable outcomes by the total number of possible outcomes.
Probability = Number of Favorable Outcomes / Total Number of Possible Outcomes
Therefore, the probability of drawing a face card that is a spade on the first draw and a king card on the second draw is:
Probability = 3/52 = 1/17 ≈ 0.06
prob(spade facecard, then king)
= (3/52)(4/52) = 3/676