Chapter 13 - Counting and Probability - 13.3 Probability - 13.3 Asses Your Understanding - Page 866: 50

$0.5$

We know that by the addition rule of probabilities: $P(A\cup B)=P(A)+P(B)-P(A\cap B).$ Hence, here we have \begin{align*} P(A\cup B)&=P(A)+P(B)-P(A\cap B) \\0.65&=P(A)+0.3-0.15 \\0.65&=P(A) + 0.15 \\0.65-0.15&=P(A)\\ 0.50&=P(A) \end{align*}