An unfair coin having probability of showing Head p is flipped 6 times. Suppose that all the tosses are independent.
(a) Determine the probability that the coin will show Head 4 times and Tail 2 times?
(b) Determine the probability that the coin will show at least 1 Head in the first 4 tosses?
(c) Suppose that there was no Head in the first 4 tosses, what is the probability that the coin will show Head for the first time at the 6th toss?
(d) Determine the probability to get second Head at the 5th toss.
Please show me how you derive the answer step by step.