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 addition rule of probability

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 as \( P(B)=P(A \cup B)-P(A)+P(A \cap B) \).

Step3: Substitute the given values

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

Step4: Calculate the result

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

Answer:

\( 0.62 \) (corresponding to the option with 0.62)