SOLUTION: A jar has 7 red marbles, 7 blue marbles and 6 white marbles. I take 3 marbles with no replacement. What is the probability that all 3 are the same color? What is the probabili

Algebra ->  Probability-and-statistics -> SOLUTION: A jar has 7 red marbles, 7 blue marbles and 6 white marbles. I take 3 marbles with no replacement. What is the probability that all 3 are the same color? What is the probabili      Log On


   

Question 1164016: A jar has 7 red marbles, 7 blue marbles and 6 white marbles. I take 3
marbles with no replacement. What is the probability that all 3 are the same
color? What is the probability that none are white?
Answer by Edwin McCravy(20064) About Me  (Show Source):
You can put this solution on YOUR website!
A jar has 7 red marbles, 7 blue marbles and 6 white marbles. I take 3
marbles with no replacement. What is the probability that all 3 are the
same color? What is the probability that none are white?
There are C(7,3) ways to choose 3 red marbles,
C(7,3) ways to choose 3 blue marbles, and
C(6,3) ways to choose 3 white marbles.

There are 7+7+6=20 marbles, so there are C(20,3) to choose three marbles.

Desired probability: 

%28%22C%287%2C3%29%22%2B%22C%287%2C3%29%22%2B%22C%286%2C3%29%22%29%2F%22C%2820%2C3%29%22%22%22=%22%220.0789473684

What is the probability that none are white?
There are 7+7=14 non-white marbles.

There are C(14,3) ways to choose 3 non-white marbles 

There are C(20,3) to choose three marbles.

Desired probability:

%22C%2814%2C3%29%22%2F%22C%2820%2C3%29%22%22%22=%22%220.3192982456

Edwin