Question

determine whether the following statement is true or false.
the probability that an event will not occur is equal to the probability that it will occur minus 1.

choose the correct answer below.
oa. the statement is true.
ob. the statement is false because the probability that an event will not occur is equal to the probability that it will occur squared
oc. the statement is false because the probability that an event will not occur is equal to 1 minus the probability that it will occur
od. the statement is false because the probability that an event will not occur is equal to 1 divided by the probability that it will occur

Explanation:

Step1: Recall the probability formula

Let \(P(A)\) be the probability that an event \(A\) occurs. The probability that the event \(A\) does not occur is denoted as \(P(\overline{A})\).
We know from the basic rules of probability that \(P(A)+P(\overline{A}) = 1\).

Step2: Solve for \(P(\overline{A})\)

From \(P(A)+P(\overline{A}) = 1\), we can solve for \(P(\overline{A})\) by subtracting \(P(A)\) from both sides of the equation.
We get \(P(\overline{A})=1 - P(A)\).

Answer:

C. The statement is false because the probability that an event will not occur is equal to 1 minus the probability that it will occur.