The probability of a student passing any examination is \( \frac{2}{3} \). The probability of not passing an examination is the complement of passing, which is \( 1 - \frac{2}{3} = \frac{1}{3} \).

Since the student takes three examinations, the probability of not passing any of them is the product of the probabilities of not passing each individual examination:

\( \left(\frac{1}{3}\right) \times \left(\frac{1}{3}\right) \times \left(\frac{1}{3}\right) = \frac{1}{27} \)

So, the probability that the student will not pass any of the examinations is 1/27.