Probability Distributions?

The number of eggs laid per pair of birds can be considered as a discrete random variable X.
P(X=0) = 0.2
P(X=x) = k(4x-x^2) for x=1,2,3,4
P(X=x) = 0 otherwise

Probability of at least one egg surviving depending on number of eggs in nest (x):
Where x=1, probability of survival is 0.8
Where x = 2, probability of survival is 0.6
Where x = 3 probability of survival is 0.4

Find the probability distribution of number of chicks surviving per pair of adults in a table

As you've written it, there is insufficient information.

E.g. If two eggs are laid, you have the probability of at least one surviving, but you don't have the probability of exactly 1 surviving, or exactly 2 surviving, so you can't work out the distribution of the number of chicks surviving.

Can you link/scan/photo the original question?

Yeah I put itin the original post now.

OK. That final table is the probability of an egg surviving to become a chick, for each egg. Not the probabilty of at least one surviving.

So, what have you done, any thoughts, and where are you stuck.

So I've completed the first part and got:

When x=0, P(X=x) = 0.2
When x=1, P(X=x) = 0.24
When x=2, P(X=x) = 0.32
When x=3, P(X=x) = 0.24

I'm probably still struggling to interpret the last table. When there are three eggs, isn't the probability of an egg surviving the same as the probability of at least one surviving? Or is it only one egg surviving?

The final table is the probability of a given egg surviving. You are interested in the actual number of eggs surviving.

So, for example, if there were 3 eggs, and probability of an egg surviving is 0.8 say, then the probability of all 3 eggs surviving to become chicks is 0.8^3.

There is quite a bit of calculation involved in the full answer invovling a few small binomials.

Let me know if you need more.