Investment and probability Being a mathematician, I am familiar with probability calculations, but I need to ask a question related to investments and probability, and how this is handled seen from an economics view.

Given a project which involves two tasks, task 1 and task 2. Developing task 1 cost X dollars, while developing task 2 takes Y dollars if developed at the same time as task 1 and Z dollars if developed at a later stage.

The probability that we actually need Task 2 i 70%

What is the the "probable cost" of implementing Task 1 and 2 at the same time. vs. Task 1 and then Task 2 with a certain probability.
And what is this called in economics? Probable cost? Estimated cost??
The simplest thing is to calculate the expected cost in the two scenarios:

Scenario 1: Develop both at the same time
$$E[cost]= X + Y$$

Scenario 2: Wait and see if task two is needed
$$E[cost]= X + 0.7Z$$

However I would not say expected value calculation represents the "economics view". The general view rather depends on your preferences, often expressed as utility functions. It could be your utility is a function of expected value, but it could also not be the case. What is your risk tolerance? Some people seem risk-seeking. Are you ok with a a small possibility of ruin (bankruptcy)? Preferences can also depend on reference points and more... 

For other simplistic approaches you could start with value at risk.