Question

when planning a cruise, you have a choice of 2 destinations: Cozumel (C) or Jamaica (J); a choice of 2 types of rooms: balcony (B) or inside view (I); and a choice of 4 types of excursions: water sports (W), horseback riding (H), parasailing (P), or zip lining (Z). If you are choosing only one of each, list the sample space in regard to the vacations (combinations of destinations, rooms, and excursions) you could pick from.

Answer 1

To determine the possible combinations of destinations, types of rooms, and types of excursions you can construct a tree diagram listing all options.

-Start with the destinations Cozumel (C) and Jamaica (J)

-Then write the type of hotel room Balcony (B) or Inside view (I)

-Finally, list for each option the four types of excursions Water sports (W), Horseback riding (H), Parasailing (P), and Ziplining (Z)

The diagram is like this:

There are a total of 16 possible combinations between destinations, rooms, and excursions that form the sample space, you can list it as follows:

S={CBW, CBH, CBP, CBZ, CIW, CIH, CIP, CIZ, JBW, JBH, JBP, JBZ, JIW, JIH, JIP, JIZ}