lgbasallote 3 years ago Three cards are given to you from a well-shuffled deck of cards. What is the probability that you get all 3 cards from the same suit?

1. satellite73

thirteen choose three over fifty two choose three

2. satellite73

times four

3. lgbasallote

is this $\frac 1{52 C3}$

4. KingGeorge

Try the method I was talking about a little earlier.

5. KingGeorge

You first need to find the possible ways you can choose three cards from the same suit, and then divide by all the possible three card hands. So you have Construction: Choices: 1. Choose a suit $$\binom41$$ and then 2. Choose a 3 card set from 13 $$\binom{13}{3}$$ So there are $\binom41\cdot\binom{13}{3}$3card hands where all the cards are from the same suit.

6. lgbasallote

so the probability would be $\frac 1{4 C 1 \times 13 C 3}$

7. KingGeorge

Now we need to find all 3 card hands total. This is just $$\binom{52}{3}$$ (it's a one step process with how I was doing it before). Thus, your probability would be $\Large P=\frac{\binom{4}{1}\cdot\binom{13}{3}}{\binom{52}{3}}$

8. lgbasallote

probability is.... the possible events over the total right?

9. KingGeorge

We have to divide by the total number of hands to find probability.

10. KingGeorge

Right.

11. lgbasallote

oh. i get the logic now

12. lgbasallote

thanks

13. KingGeorge

You're welcome.