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>ARE THEY INDEPENDENT

Yes:

>20% chance of receiving an offer from **each** of the companies
>
>MUTUALLY EXLUSIVE

See here:

>receive at least one offer

So it really doesn't matter if they're exclusive, he only wanted one successful interview anyway.

>ETC?!?!?!

Like what?
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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%**

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