# What is the probability of drawing 2 or 3 jacks

1. Dec 18, 2005

### Atomos

I am conviced that the answer provided in the key is wrong:

What is the probability of drawing 2 or 3 jacks from a standard deck of cards without replacement.

P(3jacks or 2jacks) = P(3jacks) + P(2jacks)
= P(J)P(J|J)P(J|(J|J)) + P(J)P(J|J)*(3!/2!)
= 1/5525 + 72/5525
= 73/5525 != 0.217

What am I doing wrong? And 0.217 seems absurdly high.

Last edited: Dec 18, 2005
2. Dec 18, 2005

### vaishakh

What does 2 or 3 jacks mean? how many cardsare you taking from the deck andhow many cards needs to be jack?

3. Dec 18, 2005

### Atomos

Sorry, 3 cards are being drawn.
3 jacks means 3 cards you you have drawn are jacks, 2 jacks means 2 cards you have drawn are jacks.

4. Dec 18, 2005

### vaishakh

That means there should be two answers. we are finding the probability of taking any two or three of the four existing card from 52.
First find the number of combinations of any three cards from the deck. then find the number of possibilites of taking three cards from 4. Divide to get the firstanswer of three possible cards. Ask if you didn't follow the logic behind.
Similarly continue with the next question.

5. Dec 18, 2005

### Atomos

(4C3 / 52C3) + (4C2 / 52C4)*50 ?
That does not yeild the correct answer.

6. Dec 19, 2005

### vaishakh

4C3/52C3 is correct. The second answer give a thought once more. I will help you if you still cannot. I know that is the difficult task. Please have a serious thought and reply within a day if you cannot point out your defect.

7. Dec 19, 2005

### HallsofIvy

Are you certain that the question is "two or three jacks if you draw three cards"? What about "a 5 card poker hand having either two or three jacks"?

8. Dec 19, 2005

### Atomos

arg...

4C2 * 48 / 52C3

I am getting 0.0132, which is the correct answer. I have verified this with several of my colleagues. The answer key is wrong.