1. Charles didn’t really know the reason why his son was in a bad mood, but he guessed that perhaps he had gotten some bad grades. Charles’ s guess was a shot in the dark.
2. I don’t know what they would like for a wedding gift, but we could take a shot in the dark and get them something for the kitchen.

The expression suggests that the probability of a correct guess is as small as the probability of hitting something that one shoots at in the dark.