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Discrete Probability
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 \(100a\)?
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.