Question

A coin is tossed thrice. Let the event E be the first throw results in a head and the event F be the last throw results in a tail. Find whether the events E and F are independent. Select the correct answer from above options

Answer 1

When a coin is tossed three times, the sample space is given by `S={HHH, HHT, HTH, THH, T TH, THT, HT T, T T T}`. Now, `E=` event that the first throw results in a head. `:. E={HHH, HHT, HTH, HT T}`. And, `F=` event that the last throw results in a tail. `:. F={HHT, THT, HT T, T T T}`. So, `(E nn F)={HHT, HT T}`. Clearly, `n(E)=4, n(F)=4, n(E nn F)=2` and `n(S)=8`. `:. P(E)=(n(E))/(n(S))=4/8=1/2, P(F)=(n(F))/(n(S))=4/8=1/2` and `P(E nn F)=(n(E nn F))/(n(s))=2/8=1/4` thus, `P(E nn F)=P(E)xxP(F)` Hence, E and F are independent events.