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. ( \bigcirc mathrm{a} ). ( e ) and ( g={quad} ) (use a comma to separate answers as needed.) ( \bigcirc mathrm{b} ). ( e ) and ( g={} )

Explanation:

Step1: Find intersection of E and G

The intersection of two sets \(E\) and \(G\), denoted as \(E\cap G\) (or \(E\) and \(G\)), is the set of all elements that are in both \(E\) and \(G\).
Set \(E = \{8,9,10,11,12\}\) and set \(G=\{13,14,15,16\}\).
There are no common elements between \(E\) and \(G\).

Step2: Check mutual - exclusivity

Two events \(E\) and \(G\) are mutually exclusive if \(E\cap G=\varnothing\) (the empty set).
Since \(E\cap G = \{ \}\), they are mutually exclusive.

Answer:

B. \(E\) and \(G=\{\}\); Yes, \(E\) and \(G\) are mutually exclusive.