sentence1: Alice has two coins in her pocket , a fair coin -LRB- head on one side and tail on the other side -RRB- and a two-headed coin . She picks one at random from her pocket , tosses it and obtains head . What is the probability that she flipped the fair coin ?
sentence2: A jar has 1000 coins , of which 999 are fair and 1 is double headed . Pick a coin at random , and toss it 10 times . Given that you see 10 heads , what is the probability that the next toss of that coin is also a head ?