Question

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

Answer 1

`S=\lbrace FBM,FBA,FTM,FTA,VBM,VBA,VTM,VTA\rbrace`

1) Given that the sample space is the number of total outcomes, we can tell that for that salad there are mushrooms, asparagus, bacon, eggs, french and vinaigrette

2) Notice that there are dressings and toppings. So that'll give us a set with 8 elements: s=2³=8 three outcomes and we can write this.

`\begin{gathered} M,A,B,E \\ s=\lbrace MB,ME,AB,AE\rbrace \\ \\ +1topping:F\:or\:V \\ \\ s=\lbrace FBM,FBA,FTM,FTA,VBM,VBA,VTM,VTA\rbrace \end{gathered}`

Note that there are 8 elements in this set, from the first part we get 2²=4 elements. From the 2nd part to the 3rd one we get 8 elements.