A coin is tossed thrice, and events E and F are defined as:
E : “The first throw results in a head”
F : “The last throw results in tail”
Then, which of the following statements is true for events E and F?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → E and F are independent events
There are 8 equally likely outcomes. E has 4 of them (HHH, HHT, HTH, HTT), F has 4 (HHT, HTT, THT, TTT), and both happen in HHT and HTT:
\( \displaystyle P(E)=\frac{4}{8}=\frac{1}{2} \)
\( \displaystyle P(F)=\frac{4}{8}=\frac{1}{2} \)
\( \displaystyle P(E\cap F)=\frac{2}{8}=\frac{1}{4} \)
Since \( P(E\cap F)=P(E)\,P(F) \), E and F are independent.
They are not exhaustive: TTH has neither a head first nor a tail last.
They are not mutually exclusive: HHT is in both.