Question

(a) for each event in the table, check the outcome(s) that are contained in the event. then, in the last column, enter the probability of the event. (b) subtract. 1 - p(not x) = (c) select the answer that makes the equation true. 1 - p(not x) is the same as

Explanation:

Step1: Understand the problem

We need to find the probability of event \(X\) and \(not\ X\) based on the given table.

Step2: Calculate \(P(X)\)

From the table, \(P(X)=\frac{4}{5}\) (sum of probabilities of outcomes where \(X\) occurs: \(\frac{4}{5}\)).

Step3: Calculate \(P(not\ X)\)

We know that \(P(not\ X)=1 - P(X)\). Substituting \(P(X)=\frac{4}{5}\), we get \(P(not\ X)=1-\frac{4}{5}=\frac{1}{5}\).

Step4: Check the relationship \(1 - P(not\ X)\)

\(1 - P(not\ X)=1-\frac{1}{5}=\frac{4}{5}\), and \(P(X)=\frac{4}{5}\).

Answer:

(a) For event \(1\): check the box for \(not\ X\). For events \(2\), \(3\), \(4\), \(5\): check the box for \(X\). \(P(X)=\frac{4}{5}\), \(P(not\ X)=\frac{1}{5}\).
(b) \(1 - P(not\ X)=\frac{4}{5}\) and \(P(X)=\frac{4}{5}\), so \(1 - P(not\ X)=P(X)\).
(c) \(1 - P(not\ X)\) is the same as \(P(X)\).