The probability of a problem being solved by $3$ students independently are $\frac{1}{2}, \frac{1}{3}$ and $\alpha$ respectively. If the probability that the problem is solved is $P\left(S\right)$, then $P\left(S\right)$ lies in the interval (where, $\alpha \in \left(0,1\right)$)

• A

  $\left(0,\frac{1}{2}\right)$
• B

  $\left(\frac{1}{3},\frac{1}{2}\right)$
• Correct answer
  C

  $\left(\frac{2}{3},1\right)$
• D

  $\left(\frac{1}{3},\frac{2}{3}\right)$

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