Discrete Mathematics
# Discrete Probability

Let $X$ be the number of televisions for a household chosen randomly. It is given that

$\begin{aligned} P(X=1) & = 0.18, \\ P(X=2) & = 0.36, \\ P(X=3) & = 0.34, \\ P(X=4) & = 0.08, \\ P(X=5) & = 0.04. \end{aligned}$

If $P(X < 5) = a$, what is the value of $100a$?

In a group of $120$ students, $7$ have black hair, $35$ have blond hair, $12$ have red hair, and the remaining have brown hair. If a student is selected uniformly at random from the group, the probability that the student has black hair or blond hair can be expressed as $\frac{a}{b}$, where $a$ and $b$ are coprime positive integers. What is the value of $a+b?$

**Details and assumptions**

Each student has exactly one hair color.