A coin is tossed thrice and all eight outcomes are assumed equally likely. Find whether the events E and F are independent or not ?
E : the number of heads is odd.
F : the number of tails is odd.
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When a coin is tossed three times, the sample space is given by
S = [HHH, HHT, HTH, THT, THH, HTT, TTH, TTT]
E = {HHH, HTT, THT, TTH}, F = {TTT, HTH, THH, HHT}
E ∩ F = ϕ
P(E) = \(\frac{4}{8}\) = \(\frac{1}{2}\), P(F) = \(\frac{4}{8}\) = \(\frac{1}{2}\), P(E ∩ F) = ϕ
P(E) . P(F) = \(\frac{1}{2}\) x \(\frac{1}{2}\) x \(\frac{1}{4}\) ≠ P(E ∩ F)
∴ E and F are not independent events.