MATH 350 Homework 03

1. Let $A, B \subseteq S$. Suppose that $\mathbb{P}[A] = 0.25, \mathbb{P}[B] = 0.84$, and $\mathbb{P}[A \cap B] = 0.17$. What is the probability that $A$ or $B$ but not both occur?
2. During the first week of the 2023 fall semester at Chico State, the movie Big Boss Baby was shown twice. Among the entering class of 5,524 students, 1039 saw the movie the first time, 823 students saw the movie the second time, and 3,783 did not see the movie either time. How many students saw the movie twice?
3. Define the events $A, B, C$ as $$A = \{ x: 0 \leq x \leq 3.4 \}$$ $$B = \{ x: 2.3 \leq x \leq 5.1 \}$$ $$C = \{ x: x = 0, 1, 2, \ldots \}$$

   Find $A \cap B \cap C$.

4. Let $\mathbb{P}$ be a uniform distribution over an American roulette wheel. Let the event $A$ be that the ball drops in a pocket with number less than $10$ or greater than $30$? Write out your answer both in symbols, using cardinality, and numbers, as a fraction.
5. Consider the following table giving counts for the types of each coffee purchased at my favorite coffee shop within a weekend.

   	Small	Medium	Large
   regular	19	23	22
   decaf	20	15	17

   1. What is the probability that someone orders a small cup of coffee?
   2. What is the probability that someone orders a decaf cup of coffee?
6. Let $A$ and $B$ be independent events with $\mathbb{P}[A] = 0.62$ and $\mathbb{P}[B] = 0.3$. Find
   1. $\mathbb{P}[A \cap B]$
   2. $\mathbb{P}[A \cup B]$