Does random sampling implies non-biased results? Let's say that we want to estimate how much deforestation is done in the world considering 2 moments in time. We have a satellite that can take pictures anywhere in the world, but not of the entire world (or we're not willing to wait for the entire world to be pictured; I know there's a million better ways to do this, but let's ignore that for now).
Let's say that we take 10.000 pictures at random places on earth at moment A and 10 years later we take pictures of the same locations at moment B. Then someone manually goes through these 20.000 pictures and say deforestation/not-deforestation.
Obviously, there's going to be a bunch of pictures that were ocean at moment A, and were still ocean at moment B, which will be marked as not-deforestation.
Would the results of such a method be biased towards not-deforestation or just inaccurate because we did random sampling (which is supposed to always be unbiased) and we should have just increased the sampling size to increase accuracy?
My intuition tells me that the results would be biased because not-deforestation pictures would have a known higher chance of being selected when compared to deforested pictures, but I would like a more statistically sound argument, or perhaps to be shown why am I wrong.
Edit: I am not asking whether this would be a good method of detecting deforestation. Deforestation is just an example that suits the question because a large part of the sampling population (the entire world) is clearly not deforestation because it's water.
Let's consider the following definitions:
point A ---|--- point B ---|--- change class
forest -----|-- not forest -|--- deforestation
forest -----|-- forest ------|--- not deforestation
not forest-|-- not forest -|--- not deforestation
not forest-|-- forest ------|--- not deforestation
All the answers give a slightly different perspective on the matter, which helped me a lot to understand the problem. I will mark Tim's answer as the correct answer because he had the most contributions for my understanding, but I encourage everyone interested in this question to also read @Peter Flom's, @Lewiam's, and @bi_scholar's answers for a complete understanding.
 A: This has nothing to do with random sampling, but with using inaccurate definitions. You cannot count pictures containing ocean as "no deforestation", because, at least as I understand it, deforestation is the activity of removing forest, so if there was no forest, it couldn't be removed.
By random sampling, we mean sapling randomly from the population of interest. In your case, the population is areas that contained forest at time point A. You should gather images of such areas.
If you want to collect images of the whole globe hoping to catch areas that contain forest, then this would extremely inefficient. Quick googling suggests that approximately 8% of Earth's area are forests, so with such sampling you would need at least ten times more of the images. In such case, you would throw away over 90% of the data that did not contain any forest at time A.
Given your comment, that this is an abstract example for learning pourposes, I guess that what you're asking is if the fact that you are sampling the images from the whole Earth, while caring only about the small fraction of them, would it make the results biased "because not-deforestation pictures would have a known higher chance of being selected". If 8% of Earth's area are forests, then at time A you have 8% chance of sampling such areas, so at time A random sampling would not introduce any bias. At time B you would look at the same areas as at the time A, you would be looking if there was a change in the 8% of the 10 000 images (forest area at time A). The non-forest areas have highr chance of being sampled because they are more frequent, this suggests that there is no bias. The only problem is that your sample of the forest areas at time A is small, so this may influence how reliable is your estimate. 
A: Mainly to respond to the title question: No, random sampling does not imply unbiased results.
Generally in statistics "unbiased" (applied here to estimation; there are other uses of the term "unbiased" that don't fit here) means the following: The situation is that you want to estimate an unobserved population quantity or parameter, and you draw a sample. Then you compute an estimator as a function of the observations in the sample. Unbiased estimation means that the expected value of the estimator is equal to the population quantity you want to estimate. The expected value is computed from the sampling distribution of the estimator.
In fact there are several possible reasons for bias. 1) Bias may be caused by the sample. This is avoided by random sampling. 2) The chosen estimator may be biased for the quantity to estimate. 3) There may be issues with the taken measurements and the like. 2) and 3) can not be repaired by random sampling, so random sampling helps but cannot guarantee unbiased estimation.
The other answers seem to center around the question whether your estimator is an unbiased estimator of the (not directly observed) amount of deforestation in the population, addressing issue 2), maybe 3). This depends on how exactly deforestation is defined. I am not an expert on this and won't therefore comment on it, see the other answers. My answer is meant to clarify the framework and the general role of random sampling for unbiasedness.
A: Estimates of what?
That is, you have to precisely define "deforestation" before you can tell what is biased or unbiased. Yes, random sampling will give unbiased results, but you have to define the population before you can figure out what to sample. So, is the population:


*

*All points on the Earth?

*All land on the  Earth?

*All forested land on Earth?
or something else?
A: The biggest flaw in this method seems to be that the assumption that the rate of deforestation in one part of the earth is representative of the de-forestation of the whole population (earth). 
I'm not an expert on deforestation, but I'm sure that de-forestation rates in Europe differ from the ones in Africa. 
Ab better approach might be to observe the whole earth in form of pictures, sub-sample and hand-label them and then extrapolate. 
Note that I have not addressed the definition of de-forestation, which may or may not be an issue on it's own. 
A: I'd like to add two further sources of bias:


*

*Living in a part of Europe where the forests slowly grow, but that also sees some shifting of the areas (over a decade 2002 - 2012, we saw ≈ 0.4 % of land area forest -> no forest and ≈ 0.8 % of land area no forest -> forest, my region has ≈ 42 % of land area being forest), I'd like to add that also original non-forest areas need to be surveyed in order to detect new forest growth. Otherwise, you'll be biased by the fact that you are systematically overlooking the possibility of new forests growing/existing forests expanding. 

*Secondly (this is not clear to me from question and some comments). Sampling frequently involves several steps. 


*

*in your case, that may be a satellite streaming image data along it's course, and then you sampling locations from that stream. 

*in my case (analytical chemist), it's e.g.  taking field samples and then reducing them into small lab samples suitable to put into some instrument. 


In such situations, 


*

*Unbiased sampling in a previous step may be impossible to repair later on.

*or (in "lucky" circumstances), repairing bias in a previous step may be possible but may require non-random sampling.
E.g. randomly sampling p % of the images of a satellite stream would be unbiased sampling of the statellite's images, but may yield a very biased sample wrt. the earth's surface depending on the satellite's orbit. To still arrive at unbiased sampling of the earth surface you may need a particular non-uniform sampling from the satellite images.  



Last but not least, uniform random sampling wrt. the overall sampling procedure may be unbiased but it may not be an efficient sampling strategy (if efficiency is a concern).
I'd like to encourage you to look into literature about good sampling strategies for your application: A large tnumber of (2d) sampling strategies have been developed in particular for agricultural research together with guidelines in which cases which heuristics work well (and also wrt. to remote sensing). Developing a sampling strategy deserves substantial amounts of thought that takes into account the application/system under study.  
A: There are different types of bias in research. Only one is sampling bias. With random sampling, you can minimize this kind of bias but it does not mean other types of biases are avoided. For example, if you sample randomly, you may minimize self-selection bias, but other biases such as those arising from a bad questionnaire, bad sample size, or bad data analysis methods may still exist. 
