Question

Write out the sample space for the given experiment. Use the following letters to indicate each choice: M for mushrooms, O for olives, B for bacon, E for eggs, V for vinaigrette, and H for honey mustard. When deciding what you want to put into a salad for dinner at a restaurant, you will choose one of the following extra toppings: mushrooms, olives. Also, you will add one of following meats: bacon, eggs. Lastly, you will decide on one of the following dressings: vinaigrette, honey mustard.

Answer 1

Answer: {(MBV), (MBH) , (MEV) , (MEH) , (OBV), (OBH) , (OEV) , (OEH)}

Explanation:

• Sample space is a set that contains all the possible outcomes for an event.

For salad:

Choices for extra toppings (mushrooms, olives) =2

Choices for meats (bacon, eggs) =2

Choices for dressings (vinaigrette, honey mustard.)= 2

By Fundamental counting principal .

The number of different salads can be made= (Choices for extra toppings) x (Choices for meats ) x (Choices for dressings)

= 2 x 2 x 2 = 8

All the possible outcomes = (MBV), (MBH) , (MEV) , (MEH) , (OBV), (OBH) , (OEV) , (OEH)

Required Sample space would be : {(MBV), (MBH) , (MEV) , (MEH) , (OBV), (OBH) , (OEV) , (OEH)}