At its root, humans do have free will. In the example you give, the outcome will be completely random if done with multiple participants. I believe each person is wired differently in a unique way, and as a result, each of our subconscious minds will think of a number at random in different ways, some people maybe recalling a common number they use when asked this question, others maybe picking their "lucky" or "favorite" number, and I believe we are all different in this way.
However, I think in many ways, on a grander scale, that we are subconsciously coerced into taking certain paths in our lives where we believe we are doing so with free will, but it is really due to influence from our surroundings/society. For example, a student graduating from high school and picking what college they are going to attend, they believe they are doing so with free will, when in reality there are a large number of factors that go into what college you are attending that is out of your control. Suggestions from a guidance counselor, teacher, or even what school is popular to attend among your peers, all come into play when making this decision. This could be extended to jobs, career paths... etc.
In a simpler example, I've seen examples of this done with crowds of people at lets say a magic show. In this case, the performer would ask the audience to think of a shape within another shape in their mind, along with a color. The performer would then guess off the top of his head a certain combo of shapes, and the audience was amazed at the fact that almost all of them thought of the same set of shapes. They believed they were using free will to think of this combination, when in reality, the performer was drawing particular shapes in the air with his fingers while giving the instructions, and nobody noticed. It was their subconscious mind that allowed them to think of the shapes initially, but all of their subconscious minds were influenced in the same way, just without their knowledge of it.