Question

You are visiting a rainforest, but unfortunately,your insect repellent has run out. As a result, at each second, a mosquito lands on your neck with probability 0.5. If a mosquito lands, it will bite you with probability 0.2, and it will never bother you with probability 0.8, independently of other mosquitoes. What is the expected time between successive bites?

Answer 1

Explanation:

Prob at each second, a mosquito lands on your neck =0.5

Prob it bites/it lands = 0.2

Prob it does not bite/it lands = 0.8

Hence in one second prob for getting a bite =
`0.5(0.2) = 0.01`

i.e. 1/100 chance of getting bitten in one second

In 100 seconds number of bites
`=1`

Expected time between successive bites = 100