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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?

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Answer:

Step-by-step 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 = [tex]0.5(0.2) = 0.01[/tex]

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

In 100 seconds number of bites [tex]=1[/tex]

Expected time between successive bites = 100

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