Probability: 2 People Have Bags of 60 Marbles

[dnt]

two people have bags of 60 marbles, each numbered 1 though 60.

each pulls 20 marbles...what is the probability that they match at least one number.

the way i did was figure out what are the chances they match none and subtract that from 1:

1 - [(40/60)(39/59)(38/58)...(22/42)(21/41)]

is that correct?

now what if it was match at least 10 numbers...i can't figure that out.

 

[EnumaElish]

two people have bags of 60 marbles, each numbered 1 though 60.
each pulls 20 marbles...what is the probability that they match at least one number.
the way i did was figure out what are the chances they match none and subtract that from 1:
1 - [(40/60)(39/59)(38/58)...(22/42)(21/41)]
is that correct?
now what if it was match at least 10 numbers...i can't figure that out.

Your logic is correct.

Prob{at least 10 matches} = 1 - Prob{exactly 0 matches or exactly 1 match or ... or exactly 9 matches}

 

[dnt]

is my math correct for the first question?

 

[EnumaElish]

I am guessing, yes.

 

[EnumaElish]

is my math correct for the first question?

Go ahead and write out your math (express in words) for my benefit if you don't mind. Or just derive that expression from some kind of principle.

 

[dnt]

Go ahead and write out your math (express in words) for my benefit if you don't mind. Or just derive that expression from some kind of principle.

well i think it should be 1 - [(40/60)(39/59)(38/58)...(22/42)(21/41)]

which turns out to be 1 - [(40!/20!)/(60!/40!)] = 1 - [[(40!*40!)/(20!*60!)]

which is like >99.99%.

is that right?

 

[EnumaElish]

I have drawn 20 marbles. I label them A through T.

"A" has a number on it. What is the prob. that that number is not one of your 20? I think it is 40/60, that's your 1st term. I move on to B. What is the prob. that the number on B is not one of your 20? Why isn't this also 40/60?

I am slow to wrap my brain around this kind of problem so I try to be systematic.

 

[dnt]

oh because the marbles are not being replaced.

 

[EnumaElish]

Okay. Joe is holding 20 marbles in his hand. The prob. that my 1st marble isn't one of them is 40/60.

Move on to my next marble. Joe still has 20 marbles in his hand. What is the prob. that my 2nd marble isn't one of Joe's 20?

Why isn't the answer the same?

 

[dnt]

Okay. Joe is holding 20 marbles in his hand. The prob. that my 1st marble isn't one of them is 40/60.

Move on to my next marble. Joe still has 20 marbles in his hand. What is the prob. that my 2nd marble isn't one of Joe's 20?

Why isn't the answer the same?

well damn...now I am confused.

so you think it should be 1 - [(40/60)^20]? maybe that's it.