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 \( P(A \cup B) \) (probability of \( A \) or \( B \)) is \( P(A \cup B)=P(A)+P(B)-P(A \cap B) \) (probability of \( A \) and \( B \)). We know \( P(A) = 0.48 \), \( P(A \cap B)=0.21 \), and \( P(A \cup B) = 0.89 \). We need to solve for \( P(B) \).

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

From \( P(A \cup B)=P(A)+P(B)-P(A \cap B) \), we can rearrange it to \( P(B)=P(A \cup B)-P(A)+P(A \cap B) \).

Step3: Substitute the known values into the formula

Substitute \( P(A \cup B) = 0.89 \), \( P(A)=0.48 \), and \( P(A \cap B) = 0.21 \) into the formula:
\( P(B)=0.89 - 0.48+0.21 \)
First, calculate \( 0.89 - 0.48 = 0.41 \), then calculate \( 0.41+0.21 = 0.62 \).

Answer:

0.62