No, it does not. There are too few experiments to pass a judgement. However, this is an implicit assumption made by the authors of the problem.

The question is not really a probability question; it is a statistics question. Given some data, make an inference about properties concerning how the data were generated.

To solve any problem like this, an explicit'statistical model must be constructed. The model implied by the statement of the problem is a simple one:
1) Each spin is independent of the others.
2) Each spin has the same probability of landing on apple.

Given this (simple) model, then the classical statistical estimate of the probability that the spinner comes up apple is just the number of times it came up apple divided by the number of spins, as you indicated.

But this is only a statistical estimate of the probability, and might not necessarily be the exact probability. This raises a great number of questions about how close such an estimate is to the true answer, many of which are dealt with in an introductory course (or text, or website) on statistics.

Mark Huber

The problem is that we're thinking about the theoretical probability, which we can't determine from the given information and the experimental probability, which we can determine from the given information. The former is based on what should happen and the latter is the product of what has happened. The two aren't always the same and in most cases, given enough randomness inherent to the problem, are unlikely to be. As an example, let's say that you flip a coin 1000 times. The center of that distribution, which is the most likely outcome, would be 500 H/500 T, but at the same time, it's very unlikely for that to happen exactly like that since there are so many other outcomes possible. They are all less likely, but there's just so darn many of them. Anyway, if the problem said "Based on these results, what is the experimental probability of Jule's spinner landing on the apple on his next spin", then the 2/9 answer makes sense.

On a side note, if we're looking for the actual spinner itself, it's impossible. The spinner could be broken into four equal pieces, each 25% of the area of the spinner (taken radially, of course) and due to randomness and sampling variation, we got something like (5, 4, 6, 3). In case you are really curious, there's a test that you can run to see if this is possible called a chi-square test and when I ran it, those outcomes passed meaning that it is statistically reasonable that these results came from a spinner in four equal pieces. If we want to look at this as a strictly statistical question, it becomes much more complicated looking for the boundaries that would still produce these results a comfortable enough of the time. (In other words, if it could happen, but it would happen less than 5% of the time, it's not really reasonable to think that spinner produced those results.)

The problem is obviously looking for the experimental probability, but forgot to say that, so we're all expecting to be looking for the theoretical probability. Since finding the TP is impossible, we should assume that we're looking for the EP, but some explicit directions would be nice, especially for a 5th grader.