There are two mosquito species of equal distribution on a small island; however,
ID: 3170667 • Letter: T
Question
There are two mosquito species of equal distribution on a small island; however, the native species has a population size of 1200 while the non-native species has a population size of 400. In the native population, 30% of the individuals are known to carry malaria parasites. In the non-native population, 80% of the species carry the parasites. Males and females have equal probability of carrying the parasites. Presume a person on this island gets bitten by a mosquito. If a non-malaria mosquito bites the person, what's the probability that the mosquito is native (the one with a low probability of carrying the parasites)? If you knew a third piece of information, transmission of the parasites only occurs in 50% of mosquito bites, what is the probability that a mosquito that has bitten the person is native, carries the malaria parasites, and successfully transmits them? You capture 12 mosquitoes on this island. What's the probability that you capture 10 native and 2 non-native species?Explanation / Answer
P(native)=1200/(1200+400)=0.75
P(non-native)=0.25
P(malaria | native)=0.3, P(non-malaria|native)=1-P(malaria | native)=1-0.3=0.7
P(malaria | non-native)=0.8, P(non-malaria|non-native)=1- P(non-malarianon-|native)=1-0.8=0.2
first part) P(non-malaria|native)=1-P(malaria | native)=1-0.3=0.7
second part) P(native and malaria)=P(malaria | native)*P(native)=0.3*0.75=0.225
P(successfull transmission of parasites)=0.5
so required proabability =0.5*0.225=0.1125
third part) here we use binomial didtribution and with p=0.75=probability of native species and n=12
P(X=r)=Binomial distribution ,P(X=r)=nCrpr(1-p)n-r
P(X=10)=0.2323 (using ms-excel command ==BINOMDIST(10,12,0.75,0))