# Probability Question

• Aug 1st 2010, 10:57 PM
WeeG
Probability Question
Hello, I could use some help with this one...cheers !!

A big company produce boxes with a brand new machine that produce 10 boxes (with identical size) every minute, 7 black and the rest white (in random order). The machine pack the boxes in pairs in a special package right when it leave the production line. Let X be a random variable of the number of packages with 2 black boxes, in a minute.

1. Build the probability function of X.
2. Calculate the probability that out of 3 hours or producing, there will be at least
70 minutes in which there will be found exactly 3 packages with 2 black boxes.

thank you !
• Aug 2nd 2010, 11:53 PM
WeeG
I got a little bit of progress, maybe it will help...
X=2,3

P(A pair of 2 black boxes)=((3C0)*(7C2))/(10C2)=0.46666 Where C is the binomial coefficient, in the same way:
P(A pair of 2 white boxes)=0.0666
P(1 black and 1 white)=0.46666

What do I do from here ?
• Aug 3rd 2010, 10:25 PM
CaptainBlack
Quote:

Originally Posted by WeeG
Hello, I could use some help with this one...cheers !!

A big company produce boxes with a brand new machine that produce 10 boxes (with identical size) every minute, 7 black and the rest white (in random order). The machine pack the boxes in pairs in a special package right when it leave the production line. Let X be a random variable of the number of packages with 2 black boxes, in a minute.

1. Build the probability function of X.
2. Calculate the probability that out of 3 hours or producing, there will be at least
70 minutes in which there will be found exactly 3 packages with 2 black boxes.

thank you !

Is that the exact wording of the problem as set? Is there any contextual background before the question?

CB
• Aug 3rd 2010, 11:42 PM
WeeG
Yes, this is the question...I tried something else, maybe to calculate how many ways I have to set 10 boxes in a line. It didn't lead me far....