Write out the sample space for the given experiment. Use the following letters to indicate each choice: O for olives, M for mushrooms, T for turkey, S for shrimp, F for French, and R for ranch. When deciding what you want to put into a salad for dinner at a restaurant, you will choose one of the following extra toppings: olives, mushrooms. Also, you will add one of the following meats: turkey, shrimp. Lastly, you will decide on one of the following dressings: French, ranch.

Answer

To find the sample space, we need to list all possible combinations of one topping, one meat, and one dressing. There are 2 options for toppings (O, M), 2 options for meats (T, S), and 2 options for dressings (F, R). The total number of unique combinations is 2 x 2 x 2 = 8. By systematically pairing each topping with each meat and then each dressing, we get the following outcomes: 1) Olives, Turkey, French (OTF); 2) Olives, Turkey, Ranch (OTR); 3) Olives, Shrimp, French (OSF); 4) Olives, Shrimp, Ranch (OSR); 5) Mushrooms, Turkey, French (MTF); 6) Mushrooms, Turkey, Ranch (MTR); 7) Mushrooms, Shrimp, French (MSF); 8) Mushrooms, Shrimp, Ranch (MSR). Therefore, the sample space is: {OTF, OTR, OSF, OSR, MTF, MTR, MSF, MSR}.