How often will a die come up "4"? How likely is it to rain tomorrow? Probability is one of the most powerful frameworks for modeling the world around us.

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

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

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.

×

Problem Loading...

Note Loading...

Set Loading...