The results of three flips of a biased coin are observed.The probability of a head Occurring is 0.8.Consider the following events: [25]

A:at least two tails are observedB:exactly one head is observedC:exactly two heads are observed

a)List an appropriate sample space S for this experiment.b)Are the events of getting a head on flip independent for the 3 flips?Assign probabilities to the outcomes in S.

e)Is there a pair of mutually exclusive events among A, B, andC?If so,which pairs are mutually exclusive? f)Is there a pair of independent events among A, B, andC? If so, whichpairs are independent?

g) If the random variable X = number of heads in 3 flips, set up the probability distribution in table form. (calculate X=0, X=1,X=2,X=3)