It is possible to have a less than 50% track-record regarding binary decisions. However, I am doubtful that anyone could reasonably say about any particular binary decision that he/she has a less than 50% confidence in his/her choice. If he/she really thought that, then the thing to to would be to make the opposite choice at which point he/she would have a greater than 50% confidence in that particular choice.
It is possible to have a less than 50% track-record regarding binary decisions. However, I am doubtful that anyone could reasonably say about any particular binary decision that he/she has a less than 50% confidence in his/her choice. If he/she really thought that, then the thing to to would be to make the opposite choice at which point he/she would have a greater than 50% confidence in that particular choice.