Conditional probability

What the problems look like

A few statements from this skill. Answers, hints and worked solutions live in the practice session.

1. Warm-up

   For two events $A$ and $B$, a study reports $P(A) = \frac{4}{10}$, $P(B) = \frac{9}{10}$, and $P(A \cap B) = \frac{3}{100}$. To check whether $A$ and $B$ are independent, compute $P(A) \cdot P(B)$ and compare it with $P(A \cap B)$. Give the value of $P(A) \cdot P(B)$ as a fraction in lowest terms.

2. Warm-up

   For two events $A$ and $B$, a study reports $P(A) = \frac{6}{10}$, $P(B) = \frac{8}{10}$, and $P(A \cap B) = \frac{2}{100}$. To check whether $A$ and $B$ are independent, compute $P(A) \cdot P(B)$ and compare it with $P(A \cap B)$. Give the value of $P(A) \cdot P(B)$ as a fraction in lowest terms.

3. Warm-up

   For two events $A$ and $B$, a study reports $P(A) = \frac{1}{10}$, $P(B) = \frac{8}{10}$, and $P(A \cap B) = \frac{5}{100}$. To check whether $A$ and $B$ are independent, compute $P(A) \cdot P(B)$ and compare it with $P(A \cap B)$. Give the value of $P(A) \cdot P(B)$ as a fraction in lowest terms.

Problems shown under their original terms: Generated (template, solver-computed).