1. **Stating the problem:** Amoatemaa is deciding which courses to take. Given probabilities: - $P(Anatomy) = 0.30$ - $P(Biostatistics) = 0.70$ - $P(Anatomy \mid Biology) = 0.40$ We need to find: (a) $P(Algebra \cap Biology)$ (b) $P(Algebra \cup Biology)$ (c) Whether Algebra and Biology are independent (d) Whether Algebra and Biology are mutually exclusive Note: The problem mentions Anatomy and Biostatistics but asks about Algebra and Biology. We assume Algebra and Biology are the two events of interest, but no probabilities are given for Algebra or Biology directly. Since no probabilities for Algebra or Biology are given, we cannot calculate exact values for (a) and (b). We can only analyze independence and mutual exclusivity based on definitions. 2. **Formulas and rules:** - For two events $A$ and $B$: - $P(A \cap B)$ is the probability both occur. - $P(A \cup B) = P(A) + P(B) - P(A \cap B)$. - Events are independent if $P(A \cap B) = P(A)P(B)$. - Events are mutually exclusive if $P(A \cap B) = 0$. 3. **Given data is insufficient:** - No probabilities for Algebra or Biology are provided. - No joint probabilities involving Algebra and Biology are given. 4. **Answering each part:** (a) Cannot find $P(Algebra \cap Biology)$ without data. (b) Cannot find $P(Algebra \cup Biology)$ without data. (c) Independence check requires $P(Algebra \cap Biology)$ and $P(Algebra)P(Biology)$, which are unknown. (d) Mutually exclusive means $P(Algebra \cap Biology) = 0$, unknown. **Summary:** Without probabilities for Algebra and Biology, the problem cannot be solved as stated. Possibly a typo or missing data. If you provide probabilities for Algebra and Biology, I can help solve the problem.