Trouble understanding PMF tables

[Longines]

Hello all, I'm back with another basic probability question:

View attachment 3283

I know that it involves Bayes theorem somewhere, but I don't understand this question at all!

Note: This isn't an assignment question or anything like that, it's just a textbook question that I need help with.

Thank you

 

[Siron]

Hi,
Let's kick-off with question $(a)$. We have given that $X$ is a random variable such that conditionally on $\{U=u\}$, $X$ is binomial with parameters $(2,u)$.

Do you know the binomial distribution? If you do, you only need to apply it's PMF for question $(a)$.

Hint for question $(b)$: law of total probability.