document.write( "Question 885679: A box contains 4 red, 3 white, and 3 green two balls are drawn in succession without replacement. What is the probability that both balls are the same color? \n" ); document.write( "

Algebra.Com's Answer #535382 by KMST(5328) $\"\"$ $\"About$

You can put this solution on YOUR website!
Let's label the balls, so we can distinguish between balls of the same color.
\n" ); document.write( "I will label the red balls R1, R2, R3, and R4.
\n" ); document.write( "I will label the white balls W1, W2, and W3.
\n" ); document.write( "I will label the green balls G1, G2, and G3.
\n" ); document.write( "There are $\"10%2A9%2F2=45\"$ sets of two balls that could be made from those 10 balls.
\n" ); document.write( "How many same color pairs can be made?
\n" ); document.write( "with the four red balls, we can make $\"4.3%2F2=6\"$ sets of 2 red balls.
\n" ); document.write( "With the white balls, we can make 3 sets of two green balls.
\n" ); document.write( "With the green balls, we can make 3 sets of two green balls.
\n" ); document.write( "In all, we can make $\"6%2B3%2B3=12\"$ sets of two balls of the sane color.
\n" ); document.write( "Those sets, as a fraction of all possible sets of teo balls are
\n" ); document.write( " $\"12%2F45=4%2F15\"$ .
\n" ); document.write( "That $\"highlight%284%2F15%29\"$ is the probability that both balls are the same color. \n" ); document.write( "

\n" );