Suppose an unfair coin which comes up HEADS 2/3rds of time and TAILS 1/3rd of the time. Our experiment includes flipping this coin ten times and recording number of HEADS. Let A be the event that there are between 2 and 8 HEADS (Inclusive) total and let B be the event that there're exactly 5 HEADS. Calculate P(B|A). In addition, if C is the event that there are 4,5, or 6 HEADS, then calculate P(B|C).
(1) Compute the Probability of 0 HEADS.
(2) Compute the Probability of 1 HEAD.
(3) Compute the Probability of 9 HEADS.
(4) Compute the Probability of 10 HEADS.
(5) Compute P(A).
(6) Calculate P(B).
(7) Determine P(B ? A).
(8) Find out P(B|A).
(9) Find out P(C).
(10) Find out P(B|C).