Answer to Question #214194 in Statistics and Probability for FJ_Meyers

Question

Supposed the probability that a student will pass an Economics exam is 12, the probability that he will pass an Economics and Management exam is 35, and the probability that he will pass an Economics or a Management exam is 45. Find the probability that the student will pass a management exam.

Answer 1

Probabilities are between 0 and 1 inclusive. Thus, I will use 0.12 instead of 12, 0.35 instead of 35 and 0.45 instead of 45. I think it was a typing error.

Let E represent economics and M represent management.

$P(E\cup M)=P(E)+P(M)-P(E\cap M)$

$P(E)=0.12$

$P(E\cap M)=0.35$

$P(E \cup M)=0.45$

$0.45=0.12+P(M)-0.35$

$0.45+0.35-0.12=P(M)$

$P(M)=0.68$

The probability that the student will pass a management exam is 0.68.