Question 974672
First, I think about the problem and see what makes sense.  With a 50% probability, the expected value is 4.5, and 3 would not be unusual. 
alpha = 0.10, probability of rejecting Ho given that it is true.

P (0) given p=0.5 is 0.001953
P(1)  is  0.0176
P(2) is  0.0703
P(3) is 0.1641

I get a probability of 0.2539, which makes me fail to reject the null hypothesis and makes sense to me.

The only way I see "508" is if the decimal place was mistaken and p=0.508.  That would be doubling the p-value obtained.  If I am doing a 2-tail test, then I would double the p-value.  Otherwise, I would accept the p-value I obtained.  My guess is that the p-value was doubled, and the decimal point was misplaced.