Suppose you have a player from team A and a player from team B. You know that one of them has a 60% chance to make a shot and other has 40% chance to make a shot, but you are not sure which is which.
Suppose you choose 1 of the 2 players to shoot, how would you go about calculating his probability of missing.
My train of thought was that I could calculate it using law of total probability, but I got stuck along the way.
let $G$ = event that player is the better of the two
My equation was
$$ P(miss) = P(miss | G) * P(G) + (miss | \overline G) * P (\overline G) $$, but I was unsure of how to find $P(G)$
Alternatively, I thought maybe you could just average out the two chances and it would end up being 50/50, but that seemed off the mark.
Is there a better way of going about solving this or did I just miss something along the way?