MHB Trouble understanding PMF tables

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The discussion centers around understanding probability mass function (PMF) tables and their application in a textbook question involving a random variable X that follows a binomial distribution. The initial query highlights confusion regarding the use of Bayes' theorem in solving the problem. Participants suggest focusing on the PMF of the binomial distribution for the first part of the question. For the second part, the law of total probability is recommended as a guiding principle. Clarification on these concepts is essential for solving the posed questions effectively.
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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
 

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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.
 

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