Answer to Question #176035 in Statistics and Probability for Robin

Question

Suppose p = P ( A ) , q = P ( B ) , r = P ( AU B ) , what are the probability P ( A - B ) ?

Answer 1

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

$P(A \cap B)=P(A)+P(B)-P(A\cup B)=p+q-r$

$P(A-B)= P(A)-P(A\cap B)=p-p-q+r=r-q$

Answer: P(A-B)=r-q