SOLUTION: Given 300 marbles and 30 of them are black; what is the probability that if you randomly choose 6 of them (out of the 300) that 3 of them would be black. Request that you show the

Algebra.Com
Question 1200862: Given 300 marbles and 30 of them are black; what is the probability that if you randomly choose 6 of them (out of the 300) that 3 of them would be black. Request that you show the steps in the calculation. I know that this is some sort of binomial statistics problem that is probably not simple to solve unless you you the exact formula.
Answer by ikleyn(52908)   (Show Source): You can put this solution on YOUR website!
.

The total number of all possible sextuples of 300 marbles is the number of combinations of 300 marbles taken 6 at a time

     =  = 962822846700.



The number of all different triples of 30 black marbles is 

     =  = 4060.



The number of all different triples of 300-30 = 270 not-black marbles is 

     =  = 3244140.



The probability under the problem's question is

    P =  = 0.01368 (rounded).    ANSWER

Solved.

------------------

To see many other similar  (and different)  problems solved,  look into the lesson
    - Elementary Probability problems related to combinations
in this site.



RELATED QUESTIONS

There are two sets of marbles. Both have 1,000 in them. Bag 1 has 700 blue and 300 red. (answered by Edwin McCravy,robertb)
If their are 300 girls and 250 of them are right handed, what is the probability? (answered by tommyt3rd)
A jar contains 10 black marbles and 40 white marbles. a. If you randomly select a marble (answered by edjones)
A bag has ten marbles in it. Three of them are green, one of them is red, four of them... (answered by nerdybill)
A bag has ten marbles in it. Three of them are green, one of them is red, four of them... (answered by Fombitz)
A bag contains 5 black marbles, 4 red marbles, 6 green marbles, and 5 blue marbles. What... (answered by stanbon)
A bag has ten marbles in it. Three of them are green, one of them is red, five of them... (answered by ewatrrr)
A hat contains 40 marbles. Of them, 18 are red and 22 are green. If one marble is... (answered by Boreal)
Hello, I am studying for a probability test and at this rate I probably will not do well (answered by Boreal,Theo)