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1) Let S = {H, T} be the sample space associated to the fair coin-flipping. Is...

1) Let S = {H, T} be the sample space associated to the fair coin-flipping. Is {H} independent from {T}?

2) Let S = {HH, HT, TH, T T} be the sample space associated to flipping fair coin twice. Consider two events A = {HH, HT} and B = {HT, T H}. Are they independent?

3) Suppose now we have a biased coin that will give us head with probability 2/3 and tail with probability 1/3. Let S = {HH, HT, T H, T T} be the sample space associated to flipping such a coin twice. With the same events A, B as in (2). Are A, B independent

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