In Braydon's cafeteria, the meats available are beef and chicken. The fruits available are apple, pear and banana. Braydon is randomly given a lunch with one meat and one fruit. What is the probability that the lunch will include a banana?
(A) $\frac{1}{3}$
(B) $\frac{2}{3}$
(C) $\frac{1}{2}$
(D) $\frac{1}{5}$
(E) $\frac{3}{5}$
Solution 1

Choosing one meat and one fruit, the possible lunches are beef and apple, beef and pear, beef and banana, chicken and apple, chicken and pear, or chicken and banana.

Of these 6 lunches, 2 of them include a banana.

Thus when randomly given a lunch, the probability that it will include a banana is $\frac{2}{6}$ or $\frac{1}{3}$.

## Solution 2

Each of the possible lunches that Braydon may receive contain exactly one fruit.

The meat chosen for each lunch does not affect what fruit is chosen.

Thus, the probability that the lunch includes a banana is independent of the meat that is served with it.

Since there are 3 fruits to choose from, then the probability that the lunch includes a banana is $\frac{1}{3}$.

ANSWER: (A)