examday

/TMUA

Three events $A$, $B$ and $C$ each have probability $2/3$. Each pair of these events is independent.

A student writes the following argument, where $u$ is the probability that at least one of the three events occurs.

1. The probability that $A$ does not occur is $1/3$, and likewise for $B$ and $C$.
2. For any two of the events, the probability that neither occurs is $1/9$.
3. Therefore the probability that none of the three events occurs is $1/27$.
4. Hence $u=26/27$.

Which option identifies the first invalid deduction and gives the complete set of possible values of $u$?