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.

["Title: Tracking Migratory Patterns: A Study on GPS-Enabled Birds and Weather-Induced Delays", "Understanding bird migration is key to conservation and climate impact research. A recent ornithological study tracked 12 migratory birds—divided across three distinct routes—to analyze how weather anomalies affect flight delays. Among these, 4 birds followed Route A, 5 followed Route B, and 3 followed Route C, each fitted with GPS tags to record precise movement data.", "The study revealed that weather conditions significantly impacted travel delays: birds on Route A were 1.5 times more likely to delay than those on Route B, while birds on Route C faced twice the likelihood of delays compared to Route B. Importantly, delays occur independently across birds and routes, meaning the probability of delay per bird depends only on its assigned route, not others.", "Let ( p ) represent the base probability that a bird from Route B experiences a delay. Then, the delay probability for birds on Route A is ( 1.5p ), and for Route C, it is ( 2p ).", "To compute the expected number of delayed birds:\n- Route A has 4 birds, each with delay probability ( 1.5p ): expected delays = ( 4 \ imes 1.5p = 6p )\n- Route B has 5 birds, each with delay probability ( p ): expected delays = ( 5 \ imes p = 5p )\n- Route C has 3 birds, each with delay probability ( 2p ): expected delays = ( 3 \ imes 2p = 6p )", "Adding these contributions gives the total expected number of delayed birds:\n[\n6p + 5p + 6p = 17p\n]", "Thus, the expected number of delayed birds across all routes is ( 17p ). This model provides insight into how route-specific environmental factors amplify migration challenges, supporting better forecasting and conservation efforts.", "By quantifying delay risks in each pathway, researchers can anticipate disruptions and develop targeted interventions—ultimately helping protect vulnerable migratory species in an evolving climate."]