There are 10 marbles in a bag, and the marbles are either red or blue. Eric will randomly choose two marbles from the bag, without replacing the first one. If the probability of both marbles' being red is
2
15, how many RED marbles are in the bag?
Let the number of red marbles be r. Now we can write the equation: [tex]\frac{r}{10}\times\frac{r-1}{9}=\frac{2}{15}[/tex] Rearranging the above equation and simplifying gives the quadratic: [tex]r^{2}-r-12=0[/tex] which factorizes to: (r - 4)(r + 3) = 0 Therefore r = 4. there are 4 RED marbles in the bag.
