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}, event e = {7, 8, 9, 10} and event g = {12, 13, 14, 15}. assume that each outcome is equally likely. list the outcomes in e and g. are e and g mutually exclusive? list the outcomes in e and g. choose the correct answer below. a. e and g={} (use a comma to separate answers as needed.) b. e and g = are e and g mutually exclusive? a. no, because the events e and g have at least one outcome in common. b. yes, because the events e and g have no outcomes in common. c. yes, because the events e and g have at least one outcome in common. d. no, because the events e and g have outcomes in common.

Explanation:

Step1: Find intersection of E and G

The intersection of E = {7, 8, 9, 10} and G = {12, 13, 14, 15} is the set of elements that are in both E and G. Since there are no common elements, E ∩ G = {}.

Step2: Determine mutual - exclusivity

Two events are mutually exclusive if their intersection is the empty set. Since E ∩ G = {}, events E and G are mutually exclusive.

Answer:

List the outcomes in E and G: B. E and G = {}
Are E and G mutually exclusive? B. Yes, because the events E and G have no outcomes in common.