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. (c) select the answer that make 1 - p(x) is the same as

Explanation:

Step1: Count the number of outcomes for event \(X\)

Event \(X\) has 2 outcomes (outcome 1 and outcome 5).

Step2: Calculate \(P(X)\)

The total number of outcomes is 8. Using the formula \(P(X)=\frac{\text{Number of outcomes in }X}{\text{Total number of outcomes}}\), we have \(P(X)=\frac{2}{8}\).

Step3: Calculate \(1 - P(X)\)

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Step4: Recall the probability formula for complementary events

We know that \(P(\text{not }X)=1 - P(X)\) and also \(P(X)+P(\text{not }X) = 1\).

Answer:

(a) For event \(X\): check the boxes for outcome 1 and outcome 5. For event \(\text{not }X\): check the boxes for outcome 2, outcome 3, outcome 4, outcome 6, outcome 7, and outcome 8.
(b) \(1 - P(X)=\frac{6}{8}\)
(c) \(1 - P(X)\) is the same as \(P(\text{not }X)\)