the probability of event a is 0.48, the probability of event a and b is 0.21, and the probability of events…

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?\n0.09\n0.20\n0.27\n0.62

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?\n0.09\n0.20\n0.27\n0.62

Answer

Explanation:

Step1: Recall the formula

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

Step2: Rearrange the formula for $P(B)$

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

Step3: Substitute the given values

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

Step4: Calculate the result

$P(B)=0.62$.

Answer:

$0.62$