Question

A probability experiment is conducted in which the sample space of the experiment is S = {11,12,13,14,15,16,17,18,19,20,21,22). Let event E = {12,13,14,15,16,17} and event F = {16,17,18,19). List the outcomes in E and F. Are E and F mutually exclusive? List the outcomes in E and F. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. { } (Use a comma to separate answers as needed.)

Answer 1

Events E and F in the given probability experiment are not mutually exclusive since they share outcomes 16 and 17. The correct list of common outcomes for E and F is {16, 17}.

Step-by-step explanation:

The sample space for this probability experiment is S = {11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22}. Event E includes the outcomes {12, 13, 14, 15, 16, 17} and event F includes the outcomes {16, 17, 18, 19}. The outcomes in both event E and F are the numbers 16 and 17.

Two events are mutually exclusive if they cannot both occur at the same time, meaning they have no outcomes in common. In this case, E and F are not mutually exclusive events because they share outcomes, specifically the numbers 16 and 17. Therefore, the outcome list for E and F is not empty and should include these shared outcomes.

The correct choice is O A. {16, 17} as these are the outcomes that event E and F have in common.