Question

determine whether the following statement is true or false. if it is false, explain why.
the probability that event a or event b will occur is ( p(a \text{ or } b)=p(a)+p(b)+p(a \text{ and } b) ).

choose the correct answer below.

a. false, the probability that a or b will occur is ( p(a \text{ or } b)=p(a)+p(b)-p(a \text{ and } b) ).
b. true
c. false, the probability that a or b will occur is ( p(a \text{ or } b)=p(a)+p(b) ).
d. false, the probability that a or b will occur is ( p(a \text{ or } b)=p(a)cdot p(b) ).

Explanation:

The formula for the probability of \(A\) or \(B\) occurring is \(P(A\cup B)=P(A)+P(B)-P(A\cap B)\). This is because when we add \(P(A)\) and \(P(B)\), the probability of \(A\) and \(B\) (\(P(A\cap B)\)) is counted twice. So we need to subtract it once.

Answer:

A. False, the probability that \(A\) or \(B\) will occur is \(P(A\ or\ B)=P(A)+P(B)-P(A\ and\ B)\)