1. ## Probability modelling

Wassup guys.

I have this pain of a math problem that I need help with. There's this question:

"Suppose that the probability of a parent having no offspring is 1/4, and the probability of the parent having two offspring is 3/4. What's the probability that the population will die out in the 4th generation?"

The lecturer insists that there are no errors in the question, grammatical or otherwise.

Help anyone?

2. ## Re: Probability modelling

work out the probability of the 3rd generation containing 1,2,3,... pairs of adults.

Let the number of pairs of adults in generation 3 be X.
Let the size of generation 4 be Y.

Use this identity: P(y=0) = P(y=0 and x=1) + P(y=0 and x=2) + p (y=0 and x=3) ..... up to the maximum possible value of x.

Check you understand why this works.

3. ## Re: Probability modelling

Another friend gave me the idea of bacteria, where the birthing process (mitosis) would always yield two offspring, in which case we simply construct a 4-step transition matrix with the states "0" and "1" being "no offpring" and "two offsrping" respectively, then we find P^4(10)...what do you think?