How to calculate a probability of exactly?

[sbt_094]

The question
You got 30 balls and 6 cells with the numbers 1,2,3,4,5,6.
What is the probability we get in cell number 6, 29 balls exactly?
What is the probability we get in cells 1,2 exactly 29 balls?
What is the probability we get in each cell 5 balls?

I tried to use the formula [n+k-1 NCR k-1] for having the total option I can have. after I realized by drawing I can have 5 options, so for me, the answer for the first question is 5/(30+6-1C6-1). am I right about it? and about the other 2 questions, I'm kind of lost..

 

[Deleted member 4993]

The question
You got 30 balls and 6 cells with the numbers 1,2,3,4,5,6.
What is the probability we get in cell number 6, 29 balls exactly?
What is the probability we get in cells 1,2 exactly 29 balls?
What is the probability we get in each cell 5 balls?

I tried to use the formula [n+k-1 NCR k-1] for having the total option I can have. after I realized by drawing I can have 5 options, so for me, the answer for the first question is 5/(30+6-1C6-1). am I right about it? and about the other 2 questions, I'm kind of lost..

Please post the COMPLETE problem - EXACTLY. May be you could ask somebody else to translate the problem and then you post it.

 

[sbt_094]

Please post the COMPLETE problem - EXACTLY. May be you could ask somebody else to translate the problem and then you post it.

30 balls are scattered randomly between six different holes, numbered 1 2 3 4 5 6.
A. what is the porbability that hole 6 will have exactly 29 balls?
B. what is the probability that holes 1 & 2 will have a total of 29 balls exactly?
C. What is the probability of each cell having exactly 5 balls ?
and tnx

 

[Steven G]

Also do not expect someone here to solve the problem for you. This is a math help forum and not a homework service site. We expect you to be involved in solving your problem. What we offer on this forum are leading hints to get you back on track AFTER we review the attempt you made (and posted it on the forum).

 

[Steven G]

Is this the correct problem:
You have 30 balls where you will randomly place them into 6 cells, numbered 1, 2, 3, 4, 5 and 6.
What is the probability we get exactly 29 balls in cell number 6,?
What is the probability we get a total of exactly 29 balls into cell 1 and cell 2?
What is the probability we get 5 balls in each cell?

I'll help you with the 1st one. Assume that there are just 2 cells, A and B (A is like cell 6 and B is like the other 5 cells). The prob of a ball going in A is 1/6 while into B is 5/6.
The restatement of your problem is: You have 30 balls to randomly place into 2 cells, A and B. P(ball going into A)=1/6. P(B) = 5/6. Find the probability that 29 balls go into A (and 1 into B)

This is a binomial problem. Can you try it now?

 

[pka]

You got 30 balls and 6 cells with the numbers 1,2,3,4,5,6.
What is the probability we get in cell number 6, 29 balls exactly?
What is the probability we get in cells 1,2 exactly 29 balls? This is nonsense statement
What is the probability we get in each cell 5 balls?
I tried to use the formula [n+k-1 NCR k-1] for having the total option I can have. after I realized by drawing I can have 5 options, so for me, the answer for the first question is 5/(30+6-1C6-1). am I right about it? and about the other 2 questions,

I have no idea what 5/(30+6-1C6-1) could mean.
The number of ways to put thirty identical objects into six distinct cells is \(\dbinom{30+6-1}{5}=324,632\)
Now think about it: how many ways can we get in five balls in each each ?
In cell number 6, 29 balls exactly, five ways. Think about it.

 

[Steven G]

Is this the correct problem:
You have 30 balls where you will randomly place them into 6 cells, numbered 1, 2, 3, 4, 5 and 6.
What is the probability we get exactly 29 balls in cell number 6,?
What is the probability we get a total of exactly 29 balls into cell 1 and cell 2?
What is the probability we get 5 balls in each cell?

I'll help you with the 1st one. Assume that there are just 2 cells, A and B (A is like cell 6 and B is like the other 5 cells). The prob of a ball going in A is 1/6 while into B is 5/6.
The restatement of your problem is: You have 30 balls to randomly place into 2 cells, A and B. P(ball going into A)=1/6. P(B) = 5/6. Find the probability that 29 balls go into A (and 1 into B)

This is a binomial problem. Can you try it now?

Actually, there are 5 ways to place that last ball, so the above statement is not 100% correct but is surely a good starting point.