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For power modules, we need at least one of the 2 (P1 and P2). The valid combinations are: (P1 only), (P2 only), or (P1 and P2) — a total of 2² - 1 = 3 choices.
Multiply all choices: 5 × 3 × 3 = <<5*3*3=45>>45 distinct configurations.
An ornithologist tracks 12 migratory birds fitted with GPS tags. Each bird follows one of three migration routes: Route A (4 birds), Route B (5 birds), or Route C (3 birds). Due to weather anomalies, birds on Route A are 1.5 times more likely to be delayed than those on Route B, and birds on Route C are twice as likely as Route B. If delays occur independently, and each route has a base delay probability p, express the expected number of delayed birds across all routes in terms of p.
Let delay probability for Route B be p. Then Route A: 1.5p, Route C: 2p.
Expected delays:
Route A: 4 × 1.5p = 6p
Route B: 5 × p = 5p
Route C: 3 × 2p = 6p
Total expected delays = 6p + 5p + 6p = <<6+5+6=17>>17p.
#### 17p