1. **Problem statement:** Find the probability that a dolphin group is around in the morning and is partaking in social activities (f). 2. **Given:** Probability of dolphin group around in the morning $P(M)$, probability of partaking in social activities $P(S)$, and combined probabilities. 3. **Formula for intersection of two events:** $$P(M \cap S) = P(M) \times P(S|M)$$ This means the probability that both events happen is the probability of the first event times the conditional probability of the second event given the first. 4. **Calculate $P(M \cap S)$:** Given $P(M \cap S) = 0.201$ (from the problem statement). 5. **Answer for (f):** The probability that a dolphin group is around in the morning and partaking in social activities is $\boxed{0.201}$. 6. **Problem (g):** Find the probability that a dolphin group is around in the morning or is partaking in social activities. 7. **Formula for union of two events:** $$P(M \cup S) = P(M) + P(S) - P(M \cap S)$$ 8. **Calculate $P(M \cup S)$:** Assuming $P(M)$ and $P(S)$ are known or given, plug in values and subtract $0.201$. 9. **Round the final answer to 3 decimal places.** 10. **Problem (h):** Are the events "dolphin group around in the morning" and "partaking in social activities" mutually exclusive? 11. **Definition:** Events are mutually exclusive if they cannot happen at the same time, i.e., $P(M \cap S) = 0$. 12. **Check:** Since $P(M \cap S) = 0.201 \neq 0$, the events are **not** mutually exclusive. 13. **Problem (i):** Are the events "dolphin group around in the afternoon" and "partaking in social activities" independent? 14. **Definition:** Events $A$ and $B$ are independent if $P(A \cap B) = P(A) \times P(B)$. 15. **Check:** Calculate $P(A \cap B)$ and compare with $P(A) \times P(B)$. If equal, events are independent; otherwise, not. **Slug:** dolphin probability **Subject:** probability **Desmos:** {"latex":"","features":{"intercepts":true,"extrema":true}} **q_count:** 4