To find the probability that a recharge card selected at random will be either GTN or Qtel, we need to add the probabilities of selecting a GTN card and a Qtel card.

The total number of recharge cards is \(5 + 6 + 3 + 6 = 20\).

Probability of selecting a GTN card: \(\frac{\text{No. of GTN cards}}{\text{Total number of cards}} = \frac{5}{20} = \frac{1}{4}\).

Probability of selecting a Qtel card: \(\frac{\text{No. of Qtel cards}}{\text{Total number of cards}} = \frac{3}{20}\).

Now, add the probabilities:

Probability of selecting a GTN card OR a Qtel card \(= P(\text{GTN}) + P(\text{Qtel}) = \frac{1}{4} + \frac{3}{20} = \frac{5}{20} + \frac{3}{20} = \frac{8}{20}\).

Simplify the fraction:

\(\frac{8}{20} = \frac{2}{5}\).

Therefore, the probability that a recharge card selected at random will be GTN or Qtel is \(\frac{2}{5}\).