You have 100 coins, and 99 of them are fair (equal probability of heads or tails). One of them is weighted and has a 90% probability of landing on heads. You randomly choose one of the 100 coins. Find the probability that it is a weighted coin, under the following scenarios:
(a) You flip it 10 times and lands on heads 10 times (b) You flip it 10 times and it lands on heads 9 times
(c) You flip it 20 times and it lands on heads 18 times (d) You flip it 100 times and it lands on heads 77 times