ข้อสอบ PAT 1 - กุมภาพันธ์ 2563

$$\begin{gathered} \mathrm{จากสูตร} Inclusive \& Exclusive \\ n\left(A\cup B\right) = n\left(A\right)+n\left(B\right)-n\left(A\cap B\right) \\ \mathrm{จากโจทย์} \mathrm{ลบแผนภาพได้ดังรูป} \end{gathered}$$

$$\begin{gathered} n\left(A\cup B\cup C\right) = 100 \dots \overline{)1} \\ n\left[\left(A\cup B\right)-C\right] = 35 \dots \overline{)2} \\ n\left[C-\left(A\cup B\right)\right] = 9 \dots \overline{)3} \end{gathered}$$

$\mathrm{จาก} \overline{)1} - \overline{)2} :$

$$\begin{gathered} n\left(C\right) = 100-35 \\ = 65 \dots \overline{)4} \end{gathered}$$

$\mathrm{จาก} \overline{)1} - \overline{)3} :$

$$\begin{gathered} n\left(A\cup B\right) = 100-9 \\ = 91 \dots \overline{)5} \end{gathered}$$

$$\begin{gathered} \mathrm{จาก} n\left(A\right)+n\left(B\right)+n\left(C\right) = 199 \\ n\left(A\right)+n\left(B\right)+65 = 199 \\ n\left(A\right)+n\left(B\right) = 134 \dots \overline{)6} \end{gathered}$$

$$\begin{gathered} \mathrm{จาก} n\left(A\cup B\right) = n\left(A\right)+n\left(B\right)-n\left(A\cap B\right) \\ 91 = 134-n\left(A\cap B\right) \\ \mathrm{ดังนั้น} n\left(A\cap B\right) = 43 \\ \mathrm{ตอบ} 2 \end{gathered}$$