1. ## 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 !

2. 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 ?

3. 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

4. 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....