Question

(b) select the probability that is equal to p(a) + p(b) - p(a and b). options: p(a), p(b), p(a or b), p(a and b)

Explanation:

Step1: Recall Probability Formula

The formula for the probability of the union of two events \( A \) and \( B \) (i.e., \( P(A \text{ or } B) \)) is given by the addition rule of probability: \( P(A \cup B) = P(A) + P(B) - P(A \cap B) \), where \( A \cap B \) represents the event that both \( A \) and \( B \) occur (i.e., \( P(A \text{ and } B) \)).

Step2: Match with Given Expression

We are given the expression \( P(A) + P(B) - P(A \text{ and } B) \). Comparing this with the addition rule formula, we see that this is equal to \( P(A \text{ or } B) \) (since \( P(A \cup B) = P(A \text{ or } B) \) and \( P(A \cap B) = P(A \text{ and } B) \)).

Answer:

\( \boldsymbol{P(A \text{ or } B)} \) (the option corresponding to \( P(A \text{ or } B) \))