Question

the probability of event a is 0.48, the probability of event a and b is 0.21, and the probability of events a or b is 0.89. what is the probability of event b? 0.09 0.20 0.27 0.62

Explanation:

Step1: Recall the formula for the probability of the union of two events.

The formula for the probability of \( A \) or \( B \) (denoted as \( P(A \cup B) \)) is \( P(A \cup B) = P(A) + P(B) - P(A \cap B) \), where \( P(A \cap B) \) is the probability of \( A \) and \( B \).

Step2: Rearrange the formula to solve for \( P(B) \).

We can rearrange the formula to \( P(B) = P(A \cup B) - P(A) + P(A \cap B) \).

Step3: Substitute the given values into the formula.

We know that \( P(A) = 0.48 \), \( P(A \cap B) = 0.21 \), and \( P(A \cup B) = 0.89 \). Substituting these values in, we get:
\( P(B) = 0.89 - 0.48 + 0.21 \)

Step4: Calculate the result.

First, \( 0.89 - 0.48 = 0.41 \). Then, \( 0.41 + 0.21 = 0.62 \).

Answer:

0.62