Simple probability question for someone good at these things ...

[mr_lebowski]

I have a bag of 10 marbles.

3 of them are red marbles.

What is the probability I would reach in and pull out red marbles 3 out of 6 times?

Assume I choose 1 marble at a time, and put the marble chosen back in the bag each time.

TIA!

Edit: Looks like we have a consensus of 18.5%

Thanks everyone for your work!

In case you're wondering why I asked, I've finished in the Top 3 (of 10 teams) in my Fantasy Football league 3 of the 6 years my two brothers and I have held it. One of them was telling me 'that's like ... average, dude!'

And I said 'bullshit it is!'

I knew it was statistically not average, I just wanted to come back at him with hard numbers, proving my point

[RockRaven]

1. Exactly three times, or at least three times, out of the six attempts?

[mr_lebowski]

3. Well, if it's easy, what is the odds for each ...

1 time, 2 times, 3 times, etc. Out of 6 attempts.

But 3 times out of 6 exactly is what I'm most interested in.

[RockRaven]

12. If I've remembered how to do binomial probabilities correctly, here's the outcomes...

0 red - 11.8%
1 red - 30.3%
2 red - 32.4%
3 red - 18.5%
4 red - 6%
5 red - 1%
6 red - 0.07%

[Ohiogal]

2. Are you going to reveal the answer eventually?

I’ll say 27 out of 1000.

[mr_lebowski]

4. No but somebody else is ...

I honestly don't know how to calculate it that's why I ask.

[Ohiogal]

5. Mr. Ohiogal is a retired math teacher

He gave me the above answer but don’t ask me how he got it!

[mr_lebowski]

14. Two people have independently come up with 18.5%

I guess it's a good thing the old man is retired

[Ohiogal]

16. Yeah I think his skills must be a bit rusty. 😄

[mr_lebowski]

17. Happens to the best of us ...

[unblock]

6. assuming you mean exactly 3 times out of 6, i'm getting 18.522%:

(.3)^3 * (.7)^3 * 6!/(3!*(6-3)!)

.3 cubed is the probability that the first 3 pulls are red.
.7 cubed is the probability that the final 3 pulls are not red (in order to get to exactly 3 reds).
so (.3)^3 * (.7)^3 is the probability of getting exactly 3 pulls in a specific order.

but we don't care about the order, so

6! /(3!*(6-3)!) is the number of different orderings of the pulls, e.g., (1, 2, 3) pulls are red; (1, 2, 4) pulls are red, etc.
this equals 20 different orderings.

all this works out to about 18.522%.


hope i'm remembering my probability math right....

[mr_lebowski]

10. Looks like we have a consensus of 18.5%

Thanks for your work!

[Lionel Mandrake]

11. You beat me to it. n/t

[mia]

7. 1/2 x 3/10 ?

I5% of the time? I'm wondering who would like my marble collection when I die. I used to play marbles in the dirt 70 years ago with the neighborhood kids. Thanks for the memories.

[Lionel Mandrake]

8. If you mean red exactly 3 out of 6 tries,

then the answer is C(6,3) p^3 q^3 = 0.18522,
where C(6,3) = 6! / (3!)^2 = 20 is a binomial coefficient,
p = 0.3 is the probability of picking a red marble, and
q = 1 - p = 0.7 is the probability of not picking a red marble on each try.

On the other hand, the probability of 3 or more red marbles can be computed similarly, but it's a bit more complicated.

[mr_lebowski]

9. Looks like we have a consensus of 18.5%

Thanks for your work!

[Lionel Mandrake]

15. You're welcome! n/t

[sdfernando]

13. I was going to say 42.....

but then I realized that would be improbable.