Question

When planning a cruise, you have a choice of 2 destinations: Cozumel (C) or Jamaica (J); a choice of 4 types of rooms: balcony (B), inside view (I), ocean view (O), or suite (S); and a choice of 2 types of excursions: water sports (W) or horseback riding (H). 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

The sample space of the vacations includes all possible combinations of destinations, rooms, and excursions.

Step-by-step explanation:

The sample space of the vacations can be determined by listing all possible combinations of destinations, rooms, and excursions. In this case, we have 2 destinations (Cozumel and Jamaica), 4 types of rooms (balcony, inside view, ocean view, suite), and 2 types of excursions (water sports and horseback riding).

We can create the sample space by listing all possible combinations:

CCBBW, CCBBH, CCBIW, CCBIH, CCOBW, CCOBH, CCSIW, CCSIH, CJBBW, CJBBH, CJBIW, CJBIH, CJOBW, CJOBH, CJSIW, CJSIH

Therefore, the sample space for the vacations is: CCBBW, CCBBH, CCBIW, CCBIH, CCOBW, CCOBH, CCSIW, CCSIH, CJBBW, CJBBH, CJBIW, CJBIH, CJOBW, CJOBH, CJSIW, CJSIH.

Answer 2

Given

There are 2 options for a destination: Cozumel (C) or Jamaica (J)

There are 4 types of rooms : Balcony (B), Inside View (I), Ocean View (O), Suite (S)

There are two types of excursions : Water sports (W) or Horseback (H)

The sample space is a combination of all the available options and can be calculated using the formula:

`\begin{gathered} Sample\text{ space = Number of options for A }*\text{ Number of options for B }* \\ Number\text{ of options C} \end{gathered}`

Applying the formula:

`\begin{gathered} Sample\text{ space = 2 }*\text{ 4 }*\text{ 2} \\ =\text{ 16 } \end{gathered}`

The list of the combinations is shown below:

CBW, CBH, CIW, CIH , COW, COH, CSW, CSH, JBW, JBH, JIW, JIH, JOW, JOH, JSW, JSH