Kilbaha 2011 exam 1 Q8 probability

[Chazef]

okay so just before I go to bed I want to know whether I've done this question right

A binomial distribution of the random variable X, with six independent trials, is such that Pr ( X = 3) = Pr ( X = 4). If p is the probability of a success on any trial, find the value of p.

I got p=0,1,4/7 but I'm not sure if 0 or 1 are permissible, could anybody clear this up (hopefully 4/7 is actually a correct solution too)

[Lejn]

I got 4/7, too. I feel like we can't dismiss 0 or 1, because unless there's something in the question that you haven't told me, they're also right.