1. **State the problem:** We have a table showing dolphin group activities at different times of day. We want to find various probabilities related to social activities and times of day. 2. **Recall probability formula:** Probability of an event $A$ is $P(A) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$. 3. **Given data:** Total dolphin groups = 189. 4. **a) Probability dolphin group is partaking in social activities:** $$P(\text{Social}) = \frac{\text{Total social}}{\text{Total groups}} = \frac{62}{189}$$ Calculate: $$P(\text{Social}) = 0.328$$ 5. **b) Probability dolphin group is around in the afternoon:** $$P(\text{Afternoon}) = \frac{\text{Total afternoon}}{\text{Total groups}} = \frac{23}{189}$$ Calculate: $$P(\text{Afternoon}) = 0.122$$ 6. **c) Probability dolphin group is social given it is afternoon:** Conditional probability formula: $$P(\text{Social} | \text{Afternoon}) = \frac{P(\text{Social and Afternoon})}{P(\text{Afternoon})} = \frac{9/189}{23/189} = \frac{9}{23}$$ Calculate: $$P(\text{Social} | \text{Afternoon}) = 0.391$$ 7. **d) Probability dolphin group is afternoon given it is social:** $$P(\text{Afternoon} | \text{Social}) = \frac{P(\text{Social and Afternoon})}{P(\text{Social})} = \frac{9/189}{62/189} = \frac{9}{62}$$ Calculate: $$P(\text{Afternoon} | \text{Social}) = 0.145$$ 8. **e) Probability dolphin group is morning given it is social:** $$P(\text{Morning} | \text{Social}) = \frac{P(\text{Social and Morning})}{P(\text{Social})} = \frac{38/189}{62/189} = \frac{38}{62}$$ Calculate: $$P(\text{Morning} | \text{Social}) = 0.613$$ 9. **f) Probability dolphin group is morning and social:** $$P(\text{Morning and Social}) = \frac{38}{189} = 0.201$$ **Final answers rounded to 3 decimal places:** a) 0.328 b) 0.122 c) 0.391 d) 0.145 e) 0.613 f) 0.201