A marine biology research team conducted a health assessment of 200 sea turtles across three distinct foraging zones: Sandy Beach, Coral Reef, and Open Ocean. The researchers recorded the frequency of four health indicators. The distribution of turtles in each zone was 50 in the Sandy Beach zone, 80 in the Coral Reef zone, and 70 in the Open Ocean zone. The findings are summarized in the table below:
| Health Indicator | Sandy Beach | Coral Reef | Open Ocean |
|---|---|---|---|
| Plastic Ingestion | 10 | 30 | 45 |
| Barnacle Infestation | 35 | 40 | 20 |
| Shell Damage | 15 | 25 | 30 |
| Low Weight | 20 | 10 | 25 |
Calculate the probability that a turtle selected at random from the study: (i) is from the Open Ocean zone and exhibits Plastic Ingestion; (ii) exhibits Shell Damage; (iii) exhibits Barnacle Infestation, given that it was observed in the Coral Reef zone.
For the subset of turtles in the Sandy Beach zone, explain why the events 'exhibits Barnacle Infestation' and 'exhibits Low Weight' cannot be mutually exclusive.
