Pembahasan Soal Ujian Profesi Aktuaris
SOAL
Berdasarkan soal nomor 11. Tentukan probabilitas bahwa seorang yang berusia 10 tahun akan meninggal di antara usia 30 dan 45
- \(\frac{1}{{24}}\)
- \(\frac{1}{{12}}\)
- \(\frac{1}{8}\)
- \(\frac{1}{6}\)
- \(\frac{5}{{24}}\)
| Diketahui | \(S\left( x \right) = \frac{{90 – x}}{{90 + x}},0 \le x \le 90\) |
| Rumus yang digunakan |
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| Proses pengerjaan | \({}_{\left. {20} \right|15}{q_{10}} = {}_{20}{p_{10}} \cdot {}_{15}{q_{30}}\) \({}_{\left. {20} \right|15}{q_{10}} = \frac{{S\left( {30} \right)}}{{S\left( {10} \right)}} \cdot \left( {1 – \frac{{S\left( {45} \right)}}{{S\left( {30} \right)}}} \right) = \frac{{S\left( {30} \right)}}{{S\left( {10} \right)}} \cdot \left( {\frac{{S\left( {30} \right) – S\left( {45} \right)}}{{S\left( {30} \right)}}} \right)\) \({}_{\left. {20} \right|15}{q_{10}} = \frac{{S\left( {30} \right) – S\left( {45} \right)}}{{S\left( {10} \right)}}\) \({}_{\left. {20} \right|15}{q_{10}} = \frac{{\frac{{90 – 30}}{{90 + 30}} – \frac{{90 – 45}}{{90 + 45}}}}{{\frac{{90 – 10}}{{90 + 10}}}}\) \({}_{\left. {20} \right|15}{q_{10}} = \frac{5}{{24}}\) |
| Jawaban | E. \(\frac{5}{{24}}\) |