# probability question?

• Sep 26th 2007, 09:39 AM
phatus
probability question?
Hi

I wanted to know how to work something out so hopefully someone can confirm if the way i'm doing it is correct or not. It's quite a simple thing so shouldn't be to taxing. :D

If i have 47 sticks and 9 of the sticks are coloured red if i select a stick at random the chance of picking the a red stick is 19% (9 divided by 47 x 100). What i want to know is if i have two attempts to pick a red stick what is the percentage chance of me picking it?

I believe the 19% needs to be multiplied by 1.5 which would make it about a 28% chance. I'd like to know the correct way to work this out though because if the red stick isn't picked on the first attempt this means there are only 46 sticks left to choose from which would affect the result albeit only slightly so the multiply by 1.5 probably isn't the most accurate way of working it out.

Help much appreciated.
• Sep 26th 2007, 10:19 AM
CaptainBlack
Quote:

Originally Posted by phatus
Hi

I wanted to know how to work something out so hopefully someone can confirm if the way i'm doing it is correct or not. It's quite a simple thing so shouldn't be to taxing. :D

If i have 47 sticks and 9 of the sticks are coloured red if i select a stick at random the chance of picking the a red stick is 19% (9 divided by 47 x 100). What i want to know is if i have two attempts to pick a red stick what is the percentage chance of me picking it?

I believe the 19% needs to be multiplied by 1.5 which would make it about a 28% chance. I'd like to know the correct way to work this out though because if the red stick isn't picked on the first attempt this means there are only 46 sticks left to choose from which would affect the result albeit only slightly so the multiply by 1.5 probably isn't the most accurate way of working it out.

Help much appreciated.

With or without replacement?

With replacement the probability of picking a red stick on each turn is the same. Therefore the probability of not getting red on either turn is:

(38/47)x(38/47) ~= 0.654,

So the probability of getting one or more red sticks is ~= 1-0.654 = 0.346,
or ~34.6%.

Without replacement this is:

(38/47)x(37/46) ~= 0.650

So the probability of getting one or more red sticks is ~= 1-0.65 = 0.35,
or ~35.0%.

RonL
• Sep 26th 2007, 10:20 AM
CaptainBlack
Quote:

Originally Posted by phatus
Hi

I wanted to know how to work something out so hopefully someone can confirm if the way i'm doing it is correct or not. It's quite a simple thing so shouldn't be to taxing. :D

If i have 47 sticks and 9 of the sticks are coloured red if i select a stick at random the chance of picking the a red stick is 19% (9 divided by 47 x 100). What i want to know is if i have two attempts to pick a red stick what is the percentage chance of me picking it?

I believe the 19% needs to be multiplied by 1.5 which would make it about a 28% chance.

Why would you beleive that?

RonL