SOLUTION: A bag contains 8 red marbles, 3 blue marbles and 5 green marbles. If three marbles are drawn out of the bag, what is the exact probability that all three marbles drawn will be gree

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Question 1195890: A bag contains 8 red marbles, 3 blue marbles and 5 green marbles. If three marbles are drawn out of the bag, what is the exact probability that all three marbles drawn will be green?

Found 4 solutions by ikleyn, MathLover1, greenestamps, Alan3354:
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.
A bag contains 8 red marbles, 3 blue marbles and 5 green marbles.
If three marbles are drawn out of the bag, what is the exact probability
that all three marbles drawn will be green?
~~~~~~~~~~~~~ 

At the start, there are  8 + 3 + 5 = 16  marbles in the bag.

Of them, 5 marbles are green.


The probability that the first drawn marble is green equals  .

After that, we have 15 marbles in the bag with 4 green marbles.
So, the probability that the first two drawn marbles are green equals  .


Analyzing further in the same way, we find that the probability
that the first three drawn marbles are green equals 

     = reduce the fractions =  =  = .   ANSWER

Solved.

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

Ignore the solution by  @MathLover1,  since it is totally wrong.

It is a good/classic example on how this problem  SHOULD  NOT  be solved.


Avoid such errors in the future  ( ! )


////////////////////


                        After reading the post by Alan, I find it necessary to explain
                            on how to read the problem and what does it really mean.


        When such problem goes without explicit pointing on  " with or without replacement ",
        then by  DEFAULT  and by the context,  it  ALWAYS  means  " without replacement ".



Answer by MathLover1(20849)   (Show Source): You can put this solution on YOUR website!

number of red marbles =
number of blue marbles =
number of green marbles =
_________________________________________
Total number of marbles =
the exact probability that all three marbles drawn will be green =
Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


The answer from @MathLover makes no sense, since there are not 16 marbles to choose from on all three draws.

The solution from @ikleyn uses (correctly!) a basic elementary method for solving the problem, considering the probabilities that each marble selected in succession is green.

Here is another basic method for solving the problem, which will be needed when the problems get more complicated.

P = (number of ways of selecting 3 green marbles and no others) divided by (total number of ways of selecting 3 of the 16 marbles):



ANSWER: 1/56

If you are studying probability, you should be familiar with (and comfortable with) both of those basic methods.
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
With or without replacement is not specified.
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