Practice By Tag: The Law of Total Probability

Question: 2014 Fall Final - 12

1 . A bowl contains 5 blue balls, 4 red balls, and 6 green balls. We choose 2 balls uniformly at random. What is the probability that these 2 balls have the same color?

(a)

$\frac{{15 \choose 2}}{{5 \choose 2}{4 \choose 2}{6 \choose 2}}$

(b)

$\frac{{5 \choose 2} + {4 \choose 2} + {6 \choose 2}}{{15 \choose 2}}$

(c)

$\frac{{5 \choose 2}{4 \choose 2}{6 \choose 2}}{{15 \choose 2}}$

(d)

$\frac{{15 \choose 2}}{{5 \choose 2} + {4 \choose 2} + {6 \choose 2}}$