Binomial Distribution and finding the chance "p"

[l1i2l3i4]

Hi all, I've been stuck on this problem and have tried many methods to try to find the probability of success "p" but I just can't seem to find it.
From this table, which I have filled already (just not in the image), I can't seem to find "p". I've tried to use the probability formula for example 1/2 = (4C2)(p^2)(1-p)^2 but I always end up in a quadratic equation to the power of 4, which is unsolvable with my knowledge. I can't seem to figure out how to solve it. The question is to find the mean of X. Maybe I don't need an exact value of the mean of X? However the following question is to find the variance, which is VAR(X) = npq, which I figured I would need a value for "p" as the fourth and final question is also, what is the probability of getting an even number. Could anyone help me with this question or finding "p" or the mean? Thank you! P(X=4) = 31/126 As the sums of P(X=x) =1

 

[tkhunny]

31/126 is good.

What's stopping you from populating the other two rows?

You should recognize [math]\sum x\cdot p(x)[/math]. What is that?

You should recognize [math]\sum x^{2}\cdot p(x)[/math]. What is that?

Are you TOLD that this is a Binomial Distribution? p(X=3) < p(X=4) makes no sense if that is what you have been told.

 

[l1i2l3i4]

31/126 is good.

What's stopping you from populating the other two rows?

You should recognize [math]\sum x\cdot p(x)[/math]. What is that?

You should recognize [math]\sum x^{2}\cdot p(x)[/math]. What is that?

Are you TOLD that this is a Binomial Distribution? p(X=3) < p(X=4) makes no sense if that is what you have been told.

Thank you so much! Actually, last night before I headed to bed, I thought again as to why we had to solve for x⋅p(x) and x2⋅p(x), there must be some sort of relevancy. I'm not sure if I had skipped over both these or had I forgotten but now that you've pointed it out, it has refreshed my memory. Thank you so much!