In a deck of 52 cards, what is the probability of drawing 4 aces in 13 cards?

Answer 1

On this one you want to start by finding the total number of ways to choose 13 cards from a standard 52 card deck:

C(52, 13) = 52! / (13! (52 - 13)!) = 635,013,559,600

Then the number of hands with exactly 4 aces comes from taking

C(4,4) x C(48,9) = 1 x 1,677,106,649 = 1,677,106,640

because you need to draw 4 all 4 of the available aces and then in then 9 other cards out of the remaining 48 cards.

That makes the end probability here

1,677,106,640 / 635,013,559,600 = 0.002641

Answer 2

Question: The probability of drawing exactly 4 aces when drawing 13 cards from a standard 52 card deck.

What's given in the problem:

1. Standard deck of 52 cards
2. Four aces in the standard deck of cards.
3. Randomly draw 13 cards from the deck.
4. 
   

Formula used to solve the problem: Combinations formula: nCr = n! divided by r! (n-r)!

1. n is the total number of items

1. r is the number of items chosen

Probability is calculated as Number of favorable outcomes divided by Total number of possible outcomes.

How to solve:

Calculated the number of ways to choose 4 aces and 9 other cards, then divide by the total number of ways to choose 13 cards,

Step 1:

Calculate the number of ways to choose 4 aces from 4 aces.

Use the combinations formula: 4C4 = 4! divided by 4!(4-4)! = 4! divided by 4!(0)! = 1

Step 2:

Calculate the number of ways to choose 9 other cards from remaining 48 cards.

Use the combinations formula: 48C9 = 48! divided by 9!(48-9)! = 48! divided by 9!39! = 662,616,620

Step 3:

Calculate the number of ways to choose 13 cards from remaining 52 cards.

Use the combinations formula: 52C13 = 52! divided by 13!(52-13)! = 52! divided by 13!39! = 635,013,559,600.

Step 4:

Calculate the probability:

Probability = Number of ways to choose 4 aces and 9 other cards divided by Total number of

ways to choose 13 cards.

Probability = 4C4 x 48C9 divided by 52C13 = 1 x 662,616,620 divided by 635,013,559,600 = 0.001043

Solution to problem:

The probability of drawing 4 aces in 13 cards is 0.001043

I hope the mathematical calculations (step by step approach) was helpful. Please let me know if you require any more assistance. If anyone in my neighborhood is interested in setting up an in-person math tutoring session. I look forward to hearing from them. Have an amazing day. Doris H.

Answer 3

To find the probability of drawing 4 aces in a 13-card hand from a standard 52-card deck:

1. **Total Number of Ways to Draw 13 Cards:**

{52}/

{13}

2. **Number of Favorable Outcomes:**

- **Choose 4 aces from 4:** {4}/{4}=1

- **Choose 9 additional cards from the remaining 48 cards:** {48}/{9}

Number of favorable ways:

1 ×{48}/{9} = {48}/{9}

3. **Probability Calculation:**

Total Ways = {52}/{13} = 635,013,559,600

Favorable Ways = {48}/{9} = 752,875,600

Probability = {752,875,600}/{635,013,559,600} =. approx 0.00119

Thus, the probability of drawing exactly 4 aces in a 13-card hand is approximately 0.00119, or 0.119%.