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?

Respuesta :

Answer:

10 seconds

Step-by-step explanation:

The probability that a mosquito will bite you each second is given by the probability that a mosquito lands multiplied by the probability that it will bite you:

[tex]P(B) = 0.5*0.2 = 0.1[/tex]

This means that the expected number of bites is 0.1 per second. The expected time between consecutive bites is given by:

[tex]t=\frac{1}{P(B)} =\frac{1}{0.1}=10\ seconds[/tex]

The expected time between successive bites is 10 seconds.