Question

event a: the selected ball has a number from 2 to 5
event b: the selected ball is grey
event a and b: the selected ball has a number from 2 to 5 an grey
event a or b: the selected ball has a number from 2 to 5 or is grey
(b) compute the following.
$ p(a) + p(b) - p(a \text{ and } b) $
(c) select the answer that makes the
$ p(a) + p(b) - p(a \text{ and } b) = $

Explanation:

Step1: Recall the Addition Rule for Probability

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: \( P(A \text{ or } B)=P(A)+P(B)-P(A \text{ and } B) \). This formula accounts for the overlap (the intersection \( A \) and \( B \)) to avoid double - counting.

Step2: Match with the Given Expression

We are given the expression \( P(A)+P(B)-P(A \text{ and } B) \). By the addition rule of probability, this expression is equal to \( P(A \text{ or } B) \).

Answer:

\( P(A \text{ or } B) \)