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.

Lost your password? Please enter your email address. You will receive a link and will create a new password via email.

Please briefly explain why you feel this question should be reported.

Please briefly explain why you feel this answer should be reported.

Please briefly explain why you feel this user should be reported.

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.