Chapter 12 - Counting and Probability - Section 12.1 Counting - 12.1 Assess Your Understanding - Page 867: 12

$25$

Given: $n(A)=30, n(B)= 40 , n(A\cup B) = 45$. Use the formula $n(A\cup B) = n(A) + n(B) - n(A \cap B)$ to obtain: $n(A\cup B) = n(A) + n(B) - n(A \cap B) \\45 = 30+40 -n(A\cap B) \\45=70-n(A \cap B) \\n(A \cap B) = 70-45 \\n(A \cap B) = 25$ Thus, $n(A \cap B)=25$.