need a probability formula

[alphatmw]

there are X marbles in a bowl. Y number of them are red. if i pick out Z marbles, what is the probability i will have at least 1 red marble? at least 2? what about exactly 1 or 2?

[jay_shark]

For the probability you have at least 1 red marble it is best that you take the complement for when you select no red marbles .

P(r=0) = c(x-y,z)/c(x,z)
p(r=1)+p(r=2)+...+P(r=y)= 1-P(r=0) = 1-c(x-y,z)/c(x,z)

b)Since we know p(r=0) , we need to figure out p(r=1) .
c(y,1)c(x-y,z-1)/c(x,z).
So now take 1-p(r=0)-p(r=1) to get your answer .

c) Just add p(r=0)+p(r=1) since these probabilities are independent .

[PairTheBoard]

[ QUOTE ]
For the probability you have at least 1 red marble it is best that you take the complement for when you select no red marbles .

P(r=0) = c(x-y,z)/c(x,z)
p(r=1)+p(r=2)+...+P(r=y)= 1-P(r=0) = 1-c(x-y,z)/c(x,z)

b)Since we know p(r=0) , we need to figure out p(r=1) .
c(y,1)c(x-y,z-1)/c(x,z).
So now take 1-p(r=0)-p(r=1) to get your answer .

c) Just add p(r=0)+p(r=1) since these Events are mutually exlusive .

[/ QUOTE ]

FYP

PairTheBoard

[jay_shark]

Yup mutually exclusive, that's what I meant to say :P

[alphatmw]

could you explain the meaning of this:

c(x-y,z)/c(x,z)

thanks.

[jay_shark]

Here is an example .

If you want to know the number of ways of selecting 3 kids from 10 , the total number of ways this can occur is c(10,3) .If you care about the order in which you select them , then it is p(10,3) . Since in your example , we don't care about the specific order in which you select marbles so we use the C notation . In general C(x,z) is the number of ways of selecting z marbles from a bowl containing x . We must specify that x>=n for this to make any sense .

Since there are y red marbles in a bowl containing x marbles in total , it must be true that there are x-y non red marbles . We must select z from x-y non red marbles, this is just C(x-y,z) . The denominator , which is the total number of ways of selecting z from x marbles is c(x,z) . The next step is to divide the number of favorable cases over the total number of cases .

[RonMexico]

FWIW, your computational time could be avoided in most cases if you use some binomial probability tables (assuming you know how to use them after reading the previous posts).