Question

1. which formula represents the probability of either event a or event b occurring, assuming they are mutually exclusive?

a. ( p(a \text{ or } b) = p(a) - p(b) )
b. ( p(a \text{ or } b) = p(a) \times p(b) )
c. ( p(a \text{ or } b) = p(a)/p(b) )
d. ( p(a \text{ or } b) = p(a) + p(b) )

Explanation:

When two events \(A\) and \(B\) are mutually exclusive, they cannot occur at the same time. The probability of either \(A\) or \(B\) occurring is the sum of their individual probabilities.

• Option a: \(P(A\ or\ B)=P(A)-P(B)\) is incorrect. Subtraction is not the operation for mutually - exclusive "or" probability.
• Option b: \(P(A\ or\ B)=P(A)\times P(B)\) is the formula for the probability of \(A\) and \(B\) occurring (for independent events), not for mutually - exclusive "or" probability.
• Option c: \(P(A\ or\ B)=P(A)/P(B)\) has no logical basis in probability theory for mutually - exclusive "or" probability.
• Option d: \(P(A\ or\ B)=P(A)+P(B)\) is correct. For mutually exclusive events, there is no overlap (\(P(A\cap B) = 0\)), and by the addition rule \(P(A\cup B)=P(A)+P(B)-P(A\cap B)\), substituting \(P(A\cap B) = 0\) gives \(P(A\cup B)=P(A)+P(B)\).

Answer:

d. \(P(A\ or\ B)=P(A)+P(B)\)