question 1: Suppose box A has 100 gold coins and box B has 60 gold coins and 40 silver coins. I choose a box at random and pick a coin from the box at random. If the coin picked turns out to be a gold coin, what is the probability that the coin was picked from box A?

question 2: A phone with battery A runs on average 12 hours on a single charge, but runs only 8 hours on average with battery B. A store puts battery A in 80% of its phones and battery B in the rest. If you buy a phone from the store, how many hours do you expect it to run on a single charge?