Chapter 12 - Counting and Probability - Section 12.3 Probability - 12.3 Assess Your Understanding - Page 886: 49

$0.3$

The Addition Rule of Probabilities says that: $P(A\cup B)=P(A)+P(B)-P(A\cap B)$. If A and B are mutually exclusive, then $P(A\cap B)=0$. Solve for $P(B)$ in the formula above to obtain: $P(A\cup B)=P(A)+P(B)-P(A\cap B)\\ P(A\cup B)-P(A)+P(A\cap B)=P(B)\\ P(B)=P(A\cup B)-P(A)+P(A\cap B)$ Substitute the given values to obtain: $P(B)=0.85-0.6+0.05\\ P(B)=0.3$.