Question

event ( w ) consists of 14 simple events. event ( x ) consists of 11 simple events, none of which are in event ( w ). event ( y ) is the intersection of the union of events ( w ) and ( x ). which of the following statements is true? (note: given that event ( e ) consists of ( n ) simple events, ( |e| = n ).) ( \bigcirc ) a. ( |x| < |w| < |y| < |z| ) ( \bigcirc ) b. ( |x| < |w| < |z| < |y| ) ( \bigcirc ) c. ( |y| < |x| < |w| < |z| ) ( \bigcirc ) d. ( |y| < |z| < |x| < |w| )

Explanation:

Step1: Calculate the number of elements in \(Y\)

Since \(Y\) is the intersection of the union of \(W\) and \(X\), and \(W\) and \(X\) are disjoint (none of \(X\)'s simple events are in \(W\)), \(|Y| = |W\cup X|=|W| + |X|=14 + 11=25\). Let's assume \(|Z|\) is a larger - scale event (not defined in the problem, but in probability - related set - up, we can assume \(|Z|\) is the sample space. If \(W\) and \(X\) are subsets of \(Z\), and \(|Z|\) is larger than \(|W\cup X|\)). Also, \(|X| = 11\), \(|W| = 14\).

Step2: Compare the magnitudes

We have \(|X|=11\), \(|W| = 14\), \(|Y|=25\). So \(|X|\lt|W|\lt|Y|\lt|Z|\) (assuming \(|Z|\) is the sample space which contains all elements of \(W\) and \(X\)).

Answer:

A. \(|X|\lt|W|\lt|Y|\lt|Z|\)