You are presented with 500 coins. 350 of them are fair coins, while the remaining 150 land tails with probability 0.65.

Part a: If you select 60 of the coins at random, what is the probability that less than half of them are fair coins?

Part b: What is the probability that a randomly selected coin flipped once will land tails?

Part c: Consider the following procedure:

1. Select one of the coins randomly.

2. Flip the coin.

3. Record whether the coin lands heads

4. Replace the coin and throroughly mix the coins.

If this procedure is repeated 100 times, what is the probability that the number of times that the coin lands heads will be less than 40?