Question

determine whether the statement is true or false. if the statement is false, make the necessary change(s) to produce a true statement. the probability of a or b can always be found by adding the probability of a and the probability of b.

a. false, if the probabilities of events a and b are not mutually exclusive events the probability that a or b will occur is determined by adding their individual probabilities.
b. true, if probabilities of events a and b are not mutually exclusive events then the probability that a or b will occur is determined by adding their individual probabilities.
c. false, if probabilities of events a and b are not mutually exclusive events then the probability that a or b will occur is determined by adding their individual probabilities and subtracting the probability that a and b occur simultaneously.
d. true, if the probabilities of events a and b are mutually exclusive events the probability that a or b will occur is determined by adding their individual probabilities.

Explanation:

The formula for \(P(A\cup B)\) (probability of \(A\) or \(B\)) is \(P(A\cup B)=P(A)+P(B)-P(A\cap B)\) when \(A\) and \(B\) are not mutually exclusive. When \(A\) and \(B\) are mutually exclusive (\(P(A\cap B) = 0\)), then \(P(A\cup B)=P(A)+P(B)\). So the original statement is false. We need to consider the non - mutually exclusive case where we subtract the probability of the intersection.

Answer:

C. False, if probabilities of events \(A\) and \(B\) are not mutually exclusive events then the probability that \(A\) or \(B\) will occur is determined by adding their individual probabilities and subtracting the probability that \(A\) and \(B\) occur simultaneously.