Pembahasan Soal Ujian Profesi Aktuaris
| Institusi |
: |
Persatuan Aktuaris Indonesia (PAI) |
| Mata Ujian |
: |
Probabilita dan Statistika |
| Periode Ujian |
: |
Juni 2014 |
| Nomor Soal |
: |
1 |
SOAL
Jika A dan B merupakan himpunan kejadian, dan diketahui \(\Pr (A \cup B) = 1\), maka \(\Pr (A’ \cup B’)\) sama dengan …
- 0
- \(1{\rm{ }}–{\rm{ }}Pr\left( {A’} \right){\rm{ }}–{\rm{ }}Pr\left( {B’} \right)\)
- \(Pr\left( {A’} \right){\rm{ }} + {\rm{ }}Pr\left( {B’} \right)\)
- \(Pr\left( {A’} \right){\rm{ }} + {\rm{ }}Pr\left( {B’} \right){\rm{ }}–{\rm{ }}1\)
- 1
| Diketahui |
\(\Pr (A \cup B) = 1\) |
| Rumus yang digunakan |
\(\Pr (A) + \Pr (B) – \Pr (A \cap B) = 1\) |
| Proses pengerjaan |
\(\Pr (A \cup B) = 1\)
\(\Leftrightarrow \Pr (A) + \Pr (B) – \Pr (A \cap B) = 1\)
\(\Leftrightarrow \Pr (A) + \Pr (B) – 1 + \Pr (A’ \cup B’) = 1\)
\(\Leftrightarrow \Pr (A) + \Pr (B) + \Pr (A’ \cup B’) = 2\)
\(\Leftrightarrow \Pr (A’ \cup B’) = 2 – \Pr (A) – \Pr (B)\)
\(\Leftrightarrow \Pr (A’ \cup B’) = \Pr (A’) + \Pr (B’)\) |
| Jawaban |
C. \(Pr\left( {A’} \right){\rm{ }} + {\rm{ }}Pr\left( {B’} \right)\) |
