Consider three biased coins. Let the probability of getting head be $\frac{1}{3}$ and the probability of getting tail be $\frac{2}{3}$ in each of the coins. Consider the experiment of tossing the three coins one by one, and the following events:
$E: \quad$ "at least two heads show up"
$F: \quad$ "first coin shows tail".
What is the conditional probability of $E$ given that $F$ has already occured?

• A

  $\frac{1}{4}$
• B

  $\frac{4}{9}$
• C

  $\frac{2}{9}$
• Correct answer
  D

  $\frac{1}{9}$

Hence, the correct answer is option: 'D'.