On an Alaskan cruise, shore excursions are offered most days. One day's options were:

 On an Alaskan cruise, shore excursions are offered most days. One day's options were:

Kayaking to a glacier;
Hiking to a waterfall.
Cruise travelers can choose to participate in one excursion,or no excursions. A family on the cruise is divided on which activity to choose. Jack and Shirley want to kayak. Emma and Chris want to hike to a waterfall. Kelly wants to stay on the ship and read her book.

Arrange the family members in their activity choice for the day in the Venn diagram below. Then, use the Venn diagram to answer the question:

Are kayaking and hiking mutually exclusive events?

 

The kayaking and hiking shore excursion options share no participants, so they are mutually exclusive. Without the Venn diagram, we knew that cruise travelers had to choose one, or none, of the shore excursions. So, when someone chooses to kayak, they can't also hike. Therefore, there will be no shared outcomes. 

Thanks