Question

a probability experiment is conducted in which the sample space of the experiment is s = {6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17}. let event e = {7, 8, 9, 10, 11} and event f = {11, 12, 13, 14}. list the outcomes in e and f. are e and f mutually - exclusive? explain.

Explanation:

Step1: Recall mutually - exclusive definition

Two events E and F are mutually exclusive if they have no common outcomes.

Step2: Identify outcomes of E and F

Event E = {7, 8, 9, 10, 11}, Event F = {1, 2, 11, 12, 13, 14}.

Step3: Check for common outcomes

The common outcome between E and F is 11.

Since there is a common outcome (11) between events E and F, they are not mutually exclusive.

Answer:

No, because the outcome 11 is in both E and F.