Question

A probability experiment is conducted in which the sample space of the experiment is S={3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14}​, event E={4, 5, 6, 7, 8, 9} and event G={10, 11, 12, 13}. Assume that each outcome is equally likely. List the outcomes in E and G. Are E and G mutually​ exclusive

Answer 1

Events E and G are mutually exclusive because they contain different outcomes with no overlap between them. The outcomes of E are 4, 5, 6, 7, 8, and 9, and the outcomes for G are 10, 11, 12, and 13.

Step-by-step explanation:

In the given probability experiment, the sample space S is {3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14}, event E is {4, 5, 6, 7, 8, 9} and event G is {10, 11, 12, 13}.

The outcomes in event E are 4, 5, 6, 7, 8, and 9.

The outcomes in event G are 10, 11, 12, and 13.

Events E and G are considered mutually exclusive because they do not share any outcomes. Mathematically, this is because there are no elements that are in both sets E and G, meaning that E AND G = ∅ (the empty set),

so P(E AND G) = 0. In other words, if one of the events occurs, the other cannot possibly occur at the same time.