Pembahasan Soal Ujian Profesi Aktuaris
SOAL
Misal A, B, C, dan D memiliki kejadian sebagai berikut:
\(B = A’\)\(;C \cap D = \Phi \) \(P[A] = \frac{1}{4};P[B] = \frac{3}{4}\,\) \(P[C|A] = \frac{1}{2};P[C|B] = \frac{3}{4};P[D|A] = \frac{1}{4};P[D|B] = \frac{1}{8}\)
Hitunglah \(P[C \cup D]\)
- \(\frac{5}{{32}}\)
- \(\frac{1}{4}\)
- \(\frac{{27}}{{32}}\)
- \(\frac{3}{4}\)
- 1
| Step 1 |
\(P[C|A] = \frac{{P[C \cap A]}}{{P[A]}}\) \(P[C \cap A] = \frac{1}{2}\,\frac{1}{4}\,\, = \,\frac{1}{8}\) \(P[C|B] = \frac{{P[C \cap B]}}{{P[B]}}\) \(P[C \cap B] = \frac{3}{4}\,\frac{3}{4}\,\, = \,\frac{9}{{16}}\) \(P[D|A] = \frac{{P[D \cap A]}}{{P[A]}}\) \(P[D \cap A] = \frac{1}{4}\,\frac{1}{4}\,\, = \,\frac{1}{{16}}\) \(P[D|B] = \frac{{P[D \cap B]}}{{P[B]}}\) \(P[D \cap B] = \frac{1}{8}\,\frac{3}{4}\,\, = \,\frac{3}{{32}}\) | ||||||||||||||||||||||||||||||||
| Step 2 | 
\(P[C \cup D] = \frac{{11}}{{16}} + \frac{5}{{32}} – 0\)
\(P[C \cup D] = \frac{{27}}{{32}}\) | ||||||||||||||||||||||||||||||||
| Jawaban | d. \(\frac{{27}}{{32}}\) |