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 probability formula

We use the formula $P(A\cup B)=P(A)+P(B)-P(A\cap B)$.

Step2: Rearrange formula for $P(B)$

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

Step3: Substitute values

Given $P(A) = 0.48$, $P(A\cap B)=0.21$, $P(A\cup B)=0.89$. Then $P(B)=0.89 - 0.48+0.21$.

Step4: Calculate result

$P(B)=0.62$.

Answer:

D. 0.62