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 = {8, 9, 10, 11, 12} and event g = {13, 14, 15, 16}. 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. yes, because the events e and g have no outcomes in common b. no, because the events e and g have 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 at least one outcome in common

Explanation:

Step1: Understand intersection of events

The intersection of two events \(E\) and \(G\), denoted as \(E\cap G\) (or \(E\) and \(G\)), consists of the outcomes that are in both \(E\) and \(G\).
Event \(E = \{8,9,10,11,12\}\) and event \(G=\{13,14,15,16\}\).
There is no number that is in both sets. So \(E\cap G=\{\}\)

Step2: Check mutual - exclusivity

Two events \(E\) and \(G\) are mutually exclusive if \(E\cap G = \varnothing\) (the empty set).
Since \(E\cap G=\{\}\) (no common outcomes), by the definition of mutually - exclusive events, \(E\) and \(G\) are mutually exclusive.

Answer:

For the first part: B. \(E\) and \(G =\{\}\)
For the second part: A. Yes, because the events \(E\) and \(G\) have no outcomes in common