Pembahasan Soal Ujian Profesi Aktuaris
Institusi |
: |
Persatuan Aktuaris Indonesia (PAI) |
Mata Ujian |
: |
Probabilita dan Statistika |
Periode Ujian |
: |
Juni 2014 |
Nomor Soal |
: |
17 |
SOAL
Diketahui kejadian A, B dan C memenuhi hubungan sebagai berikut :
\(A \cap B'{\rm{ }} = \phi ,B \cap C'{\rm{ }} = \phi ,{\rm{ }}Pr(A’ \cap B){\rm{ }} = x,{\rm{ }}Pr(B’ \cap C){\rm{ }} = y,{\rm{ }}Pr\left( C \right){\rm{ }} = z\)
Maka Pr(A) sama dengan …
- x + y + z
- x + y – z
- y + z – x
- x – y + z
- z – x – y
Diketahui |
\(A \cap B'{\rm{ }} = \phi ,B \cap C'{\rm{ }} = \phi ,{\rm{ }}Pr(A’ \cap B){\rm{ }} = x,{\rm{ }}Pr(B’ \cap C){\rm{ }} = y,{\rm{ }}Pr\left( C \right){\rm{ }} = z\) |
Rumus yang digunakan |
\(\Pr (B \cup C’) = \Pr (B) + \Pr (C’) – \Pr (B \cap C’)\)
\(\Pr (A \cup B’) = \Pr (A) + \Pr (B’) – \Pr (A \cap B’)\) |
Proses pengerjaan |
\(\Pr (B \cup C’) = \Pr (B) + \Pr (C’) – \Pr (B \cap C’)\)
\(\Leftrightarrow 1 – \Pr (B’ \cap C) = \Pr (B) + \Pr (C’) – 0\)
\(\Leftrightarrow 1 – y = \Pr (B) + (1 – z)\)
\(\Leftrightarrow z – y = \Pr (B)\)
\(\Pr (A \cup B’) = \Pr (A) + \Pr (B’) – \Pr (A \cap B’)\)
\(\Leftrightarrow 1 – \Pr (A’ \cap B) = \Pr (A) + \Pr (B’) – 0\)
\(\Leftrightarrow 1 – x = \Pr (A) + (1 – z + y)\)
\(\Leftrightarrow z – x – y = \Pr (A)\) |
Jawaban |
e. z – x – y |