S2 Question

I haven't got much time to look at this but it looks like conditional probability to me. What is the probability that A happens given B in this case you are after P(Lives 8 days given that it has lived 3) you know a formula to do these?

P(AnB)/P(B)

Struggling to get the numerator.

Consider: $\displaystyle P(>8days|>3days)=\frac{P(>8days)}{P(>3days)}$

You have a formula for this no?

No unfortunately, I've never come across this, I'm guessing this is from S1.

P(AnB)/P(B)

Struggling to get the numerator.

You are right with this formula. Reading the question it says GIVEN a mosquito survives 3 days, find the probability it will survive AT LEAST 5 MORE days
i.e P(T>8|T>3) = [P({T>8}n{T>3})]/P(t>3)

Consider the numerator. What is t>8 n t>3, thats like saying when are BOTH conditions satisfied, well both t>8 and t>3 are satisfied for t>8 so:

P(T>8|T>3) =[P(T>8)]/[P(T>3)]

In the question, it tells you the function for the probability that a mosquito survives more than t days (that is P(T>t)) so this can be used to put the fraction above into a numerical answer

Hope this helps somewhat..

Wow, that makes sense thank you.