Solving Probability of Marbles

[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 can't find the N(A) for finding this P(A)=N(A)/N(Ω) even i think that mthis way maybe is not correct...

 

[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! )

 

[ParisSpart]

i tried this but i can't do anything...

 

[tiny-tim]

i tried this but i can't do anything...

show us how far you got

 

[ParisSpart]

the problem is that in school we don't have learn this type yet. that's why i think that the result comes out from the classic type of P(A)...but i am stucked!

 

[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? ​

 

[ParisSpart]

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

 

[tiny-tim]

its 45/200

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 !

 

[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)