SOLUTION: Hi, I am so confused with marbles probability. Can you solve and let me know how you achieved the answer to the following: A box contains 3 white, 2 red, and 4 black marbles. One

Algebra ->  Probability-and-statistics -> SOLUTION: Hi, I am so confused with marbles probability. Can you solve and let me know how you achieved the answer to the following: A box contains 3 white, 2 red, and 4 black marbles. One      Log On


   

Question 861162: Hi,
I am so confused with marbles probability. Can you solve and let me know how you achieved the answer to the following:
A box contains 3 white, 2 red, and 4 black marbles. One marble is chosen at random, and it is not black. Find the probability that it is white. (Enter your answer as a fraction.)
Thank you in advance
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
There are 3%2B2%2B4=9 marbles.
Each marble is as likely to be picked as any other marble.
Because 4%2F9 of the marbles are black,
there is a 4%2F9 probability to get a black marble.
There is a 5%2F9 probability of getting a marble that is not black.
Overall, there is a 3%2F9 probability of getting a white marble.
However, out of the 5%2F9 of the cases where the marble is not black,
there is %28%283%2F9%29%29%2F%28%285%2F9%29%29=3%2F5 of those cases, when the marble is white.

Look at it this way:
If you repeat the experiment 9 million times,
you expect to get a black marble 4 million times.
The other 5 million times the marble picked will not be black.
in fact, in 3 million of those cases the marble will be white.
That is 3million%2F%225+million%22=3%2F5 of the cases when the marble is not black.