What type of probability is this? Context
I have been wondering what this type of problem might be called for a while, and have come up with an algorithmic representation, which I am not sure is correct - can anyone shed some light on this for me? I will try to give a simplified scenario that avoids the technical use-case...
Scenario
You own two pigs that are good at finding truffles. Pig A is correctly finds one 40% of the time.  Pig B correctly finds one 30% of the time.
You take the pigs to a woodland and set them to work for the day. Assuming there are truffles to be found, what is the probability that between them at least one truffle is discovered by the end of the day?
My rationale
Previously I have represented this as the following, which could be further extended for as many 'pigs' as you have in your truffle-hunting team. $P$ is the total probability of success and $p_i$ are the individual pigs probability of success:
$$P = 1-\prod_{i}(1 - p_i)$$
For the specific example with the two pigs I present above we have $P = 1 - ( (1 - 0.3) \times (1 - 0.4) ) = 0.58$
To me, this means that the more pigs you have with some truffle hunting skills, the more likely they are to find a truffle as a team.
My question(s)


*

*Is this formulation appropriate for the problem?

*What is the above formula called, so I can learn more about it's applications?

*What is this type of probability problem called?


Many thanks for your time!
 A: *

*The rationale and the formula are correct. Well done.

*There is no particular name for this formula, or at least I have not heard it.

*There is also no name for this type of probability problems. I wouldn't even recognise a type. If I had to say something I would just say "a basic probability problem"


The description of the problem needs some work though. In particular this phrase is vague:

Pig A is correctly finds one 40% of the time

Here are some interpretations, just to give you a flavour. We can come up with many more:


*

*Every time a pig examines a root(that can be a truffle or not) is correct 40% of the time

*Every location the pig examines it finds truffles with probability 40%

*The pig finds truffles with 40% probability whenever it goes for a fixed-time expedition (say a day)


From your analysis it seems that you mean the last option, but this is not evident at all. So you have to take extra care to be clear when formulating the problem.
Another major omission is the statement that the pigs are independent in their search for truffles. Again not evident at all (and probably untrue in practice). You need to explicitly state it. Your solution is valid only if the pigs are independent.
Finally this phrase: 

Assuming there are truffles to be found,

seems superfluous. If it's not superfluous it changes the problem. Are you implying for instance that the place where they look for truffles plays a role? Of course it would in practice, but do you want to model this in the formulation of your problem? If so, then we also need an a-priori probability that the place the pigs search has truffles. If this does not matter, do not mention it at all.
A: You can denote $X_1$ to be the discrete random variable representing whether a pig correctly finds truffles with probability $p=0.4$ and not finding truffles with probability $q=1-p=0.6$. Then for $n$ pigs, assuming that the pigs act independently, you can introduce the random variable $X= X_1+\cdots+X_n$. Since $X_1$ is Bernoulli distributed then the sum $X= X_1+\cdots+X_n$ is a binomial random variable with parameters n and p. Where Let $X_1,X_2,\ldots ,X_n$ are independent Bernoulli random variables. 
A: Technical specifications should never be left out in logic. 

number line colored 40% red, 30% green, and 30% black representing mutually exclusive events adding to 100%

10 by 10 "grid" made using 4 separate grids, colored such that the green (4 by 3 grid) is the overlap of independent events A finds a truffle, and B finds a truffle, The red represents B finds a truffle, but A does not( 3 by 6 grid), the blue (4 by 7 grid) represents A finds a truffle, but B does not, and the black (7 by 6 grid) represents neither A nor B finds a truffle. Okay slight inaccuracy in its creation. 
We could also have conditional probability , which looks similar to the second picture above except, The probability of A given B wouldn't be the same percentage area as the probability of A given (not B).  
Your formulation is the second picture above. aka independent events.  It does go to 100% in theory ,  but on the condition that all events are independent of all subsets of previous events. If not, then it's conditional probability. 
