What is the expected time between bites in a jungle full of bees?

[janela]

You are in a jungle, at each second a bee lands on your arm with a probability of 0.5. Given that a bee lands on you, it will bite your arm with a probability of 0.2 and not do anything with a probability of 0.8, independently of all other mosquitoes. What is the expected time between successive bites?

 

[Krusty]

1) What is the probability that you will get bitten in a single second.

2) What distribution deals with the number of trials before a success?

3) Show some working if you want help

 

[janela]

1) What is the probability that you will get bitten in a single second.

The probability of getting bitten (event B), given the bee lands on you (event A),
is given as P(B|A)=0.2
and P(A) is given as =0.5
is it correct to say P(A|B) = P (A and B) / P(A) and solve for P(B) ,
I am not sure how to solve for P(B) though, Bayes rule? 2) What distribution deals with the number of trials before a success?
Is this asking whether it is a binomial random variable
where k is the # of bites, n is the number of seconds (as each second is a new trial)
and Px(k) = (n C k) p^k * (1-p)^(n-k)

should the correct random variable equation should be
=(nCk) * P(B)^k (1-P(B))^(n-k)

I am not sure if it makes sense to make the number of bites equal to the number of seconds to find the E[X] time between successive bites.
(both equal to 2?)

 

[EnumaElish]

You are on the correct path with the conditional prob. What you are looking for is q = P(A and B), which is the binomial probability of being bitten.