For the first question, the way I would read it is "find the probability that they BOTH detect the virus". What do you think?

Your probability value is already given in the question. p=0.1 would be the probability of a single program NOT detecting a virus.

If the question is asking to find the probability that they BOTH detect the virus, you really want to know the probability of two successes in two trials. You want to find the P(X=2)

For the second question, now it is being asked to give the probability that AT LEAST one of the three detect the virus. So now you need to find the cumulative probability that X=1, X=2, X=3, otherwise stated as the probability that X is greater than or equal to 1. You could also do this by finding the probability that X=0 and subtract that result from 1.