$.[15$ pts total$]$ The probability that a mosquito in Florida is found to be infected with a particular

disease is $0\mathrm{.}25.$ A local lab has $25$ testing kits and $($randomly$)$ collects $25$ mosquitoes. $($One kit

can only be used to test a single mosquito.$)$ Let Y be the number of mosquitos that are found to be

infected with the disease. Use R to simulate the probability distribution of Y$.$ In particular, report:

$($a$)[10$ pts$]$ A table of each possible outcome and the associated Monte$-$Carlo estimate of the

probability.

$($b$)[3$ pts$]$ A barplot of the estimated probabilities.

$($c$)[2$ pts$]$ The estimated probability the lab finds $5$ infected mosquitos.

Some ideas to approach this:

$$ The infection status of $25$ mosquitoes can be generated using mosquitoes rbinom$($n$=25,$

size$=1,$ prob$=0\mathrm{.}25).$

$$ Other useful functions that may be useful for this problem include table and barplot.