Probability

# Probability - Rule of Sum

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 $100a$?

If a 20-sided fair die with sides distinctly numbered 1 through 20 is rolled, the probability that the answer is a perfect square can be expressed as $\frac{a}{b}$ where $a$ and $b$ are coprime positive integers. What is the value of $a + b$?

In a health examination of the $72$ employees at Acme Corporation, the numbers of employees with blood type $A$ and $B$ were $11$ and $19$, respectively, and the remaining employees have blood type $O$. If one of the $72$ employees is selected uniformly at random, the probability that the person's blood type is $A$ or $B$ can be expressed as $\frac{a}{b}$, where $a$ and $b$ are coprime positive integers. What is $a+b?$

Raoul chooses an integer uniformly at random from $1$ to $34.$ The probability that his number is $6$ or $32$ can be expressed as $\frac{a}{b}$, where $a$ and $b$ are coprime positive integers. What is the value of $a+b?$

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.

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