Since the companies are all separate, I would assume independence (and that they are *not* mutually exclusive).
The probability of getting at least one offer is 1 minus the probability of not getting any offers. If there is a 20% chance of getting an offer from any given company, the probability of not getting an offer is 80%.
> P(0 offers) = 0.8^4 = 0.4096
> P(1+ offers) = 1 - P(0 offers) = 1 - 0.4096
> **P(1+ offers) = 0.5904, ~59%**