Whats the eqason for this​

In triangle △abc, ∠abc=90°, bh is an altitude. find the missing lengths. ah=4 and hc=1, find bh.

There are three bags: a (contains 2 white and 4 red balls), b (8 white, 4 red) and c (1 white 3 red). you select one ball at random from each bag, observe that exactly two are white, but forget which ball came from which bag. what is the probability that you selected a white ball from bag a?

I’ve been trying all day to figure this puzzle out. i need the work for it aswell. it is a factoring polynomials tarsia. the image is below.