I find myself struggling to find anything that would help me apply these concepts all i have for now is just these courses which are quite wonderful but i would love to see or find any problems that i could apply these to something to apply this on anyone knows a solution for this ?
Not correct. we are adding each probability of B with respect to an Ai that contributes the total probability of B. The Ai's are collectively exhaustive so you can imagine some Aj that does not have some B in it the contribution to B's total probability would be zero although its weight would be P(Aj)
it's not the average as we usually think of, but it's the average of the event P(B/Ai) happening(he says weighted because each P(Ai) is already weighted because they sum to 1)