# Probability marbles

1. Feb 23, 2013

### ParisSpart

I have another quiz and i am wondering how to solve this:

In an opaque bag 10 are identical marbles numbered from 1 to 10 and in another there are 20 identicalbe marbles numbered from 1 to 20. Take a marble at random from the bag and the first one from the second. All results of this experiment are equally possible (uniform distribution).

What is the probability the first marble indicates a number greater than the second marble?

I think that N(Ω)=200 but i cant find the N(A) for finding this P(A)=N(A)/N(Ω) even i think that mthis way maybe is not correct.....

2. Feb 23, 2013

### tiny-tim

Hi ParisSpart!

I don't think there's any really simple way of doing this …

I think you'll have to consider each value M1 of the first marble separately, and sum the P(M2 < M1 | M1 = n) for each value of n.

(alternatively, there is a way that starts by calculating P(M1 = M2), and then just uses common-sense! )

3. Feb 23, 2013

### ParisSpart

i tried this but i cant do anything.....

4. Feb 23, 2013

### tiny-tim

show us how far you got

5. Feb 23, 2013

### ParisSpart

the problem is that in school we dont have learn this type yet. thats why i think that the result comes out from the classic type of P(A)....but i am stucked!

6. Feb 23, 2013

### tiny-tim

ok, then just do it by counting …

i] how many possibilities are there altogether?

i] then list all the possibilities with M1 > M2, and count them …

what do you get?

7. Feb 23, 2013

### ParisSpart

its 45/200 thanks a lot , maybe u can help me in anither quiz ? i uploaded yesterday with theme probability quiz.... thanks!

8. Feb 23, 2013

### tiny-tim

correct!

here's another way of counting to get 45, just using common-sense …

(there's usually several ways of counting the same thing )

ignore the ones with M2 > 10

that only leaves 100

subtract the ones with M1 = M2: obviously that's 10

so that leaves you only 90 with M1 ≠ M2 and both ≤ 10 …

obviously exactly half of those 90 must have M1 > M2 !

9. Feb 24, 2013

### tiny-tim

are you ok on the other thread (seems to have disappeared)?

to write a function from {1,2,3…n} to {1,2,3…m}, you have to specify what f(1) is, what f(2) is, what f(3) is, … … … what f(n) is

once you've done all of that, the function is uniquely defined

so how many functions are there altogether (in terms of n and m)?

(if you're confused, try it for n = 2 first)