A bowl contains 5 white balls, 10 red balls, and 15 blue balls.

a. You are to randomly select two balls without replacement. You will draw one ball (and keep it outside of the bowl) and then you will draw a second ball. Is the event of drawing a red ball on the first draw independent of drawing a white ball on the second draw? Explain your reasoning.

b. You are to randomly select two balls without replacement. Let X be the random variable of the number of white balls you select. Derive the probability mass function (pmf) of X (that is to say find f(x)=P(X=x)).

c. You are to randomly select two balls without replacement. You will draw one ball (and keep it outside of the bowl) and then you will draw a second ball. Thesecondball you select is red, what is the probability that the first one was white? Show and explain your work.