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You have a cube and two colours, what is the probability that every corner has a different colour

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I guess the interviewer meant that it is not possible to have two corners of the same colour sharing the same side of a cube, because in order to have different colours for each corner we should the same number of corners and colours, so 8. If that's the case, the solution is as follows: the total number of colourings possible for all the corners of the cube is 2^8 = 256; there are two ways to pick the colour of a corner and then all the others will follow if they have to be of opposite colour when they share the same side, so we have 2 successful outcomes. Then, the answer is 2/256 = 1/128 = 0.0078125 Correct me if I'm wrong, it would be helpful.

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1st round brain teasers #1 two type of socks in a drawer, how many times do you need to take a sock from the drawer to have a matching pair? #2 one stick and one match, takes 60min to burn (non-homogenously), how can you calculate 30min? #3 you ride to shop (1km away) at 30km/h, at which speed should you drive back to reach average of 60km/h? #4 how to go from the bottom of a cube to the other upper end in the shortest way?

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