SOLUTION: A bag contains 4 red, 2 white and3 blue balls. If two balls are chosen at rand without replacement, find the probability that the balls are of the same colour.

Question 1090293: A bag contains 4 red, 2 white and3 blue balls. If two balls are chosen at rand without replacement, find the probability that the balls are of the same colour.
Answer by ikleyn(52856) (Show Source): You can put this solution on YOUR website!
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A bag contains 4 red, 2 white and 3 blue balls. If two balls are chosen at random without replacement,
find the probability that the balls are of the same color.
~~~~~~~~~~~~~~~~~~~

There are   =  =  = 6 combinations to choose two red balls.


There are   = 1 combination to choose two white balls.


There are   =  =  = 3 combinations to choose two blue balls.


Thus there are 6 + 1 + 3 = 10 combinations to choose two balls of the same color.


The entire space of events is   =  =  =  = 36 combinations to choose two balls from the bag containing 4 + 2 + 3 = 9 balls.


Therefore, the probability that the balls are of the same color is   = .

Solved.

About combinations and about these magic numbers you can read from the lessons
    - Introduction to Combinations
    - PROOF of the formula on the number of Combinations
    - Problems on Combinations
in this site.

Also, you have this free of charge online textbook in ALGEBRA-II in this site
    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic "Combinatorics: Combinations and permutations".

Also see the lesson
    - Elementary Probability problems related to combinations
from the same online textbook.

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