The Monty Hall (MH) problem is a well-known and powerful cognitive illusion that illustrates how flawed human understanding of probability can be. The intuitive solution to this dilemma suggests that it doesn't matter whether the contestant switches their choice or sticks with their initial selection, as the odds of winning appear to be equal. However, switching is actually the more rational option since the probability of winning is doubled in that case. The aim of this research was to examine the transfer of knowledge regarding the structure of the Monty Hall problem and whether that knowledge affects the participants' confidence in their answers. The study involved 252 participants aged between 15 and 59 years (M=26, SD=7.24). The research was conducted online. Firstly, participants solved the classic Monty Hall problem and then one task from the standard and non-standard versions each. Participants were randomly divided into four conditions that differed based on the type of instruction/explanation provided after the classic version of the task - a control condition, a condition with an explanation of the problem, a condition with a suggestion to think about a similarly posed problem, and a condition with an explanation of the problem and a suggestion to think about similar problem. Participants in the conditions with the presented explanation were significantly more successful in solving the standard version of the task. However, there was no transfer of knowledge observed in the non-standard version of the task, indicating a lack of deeper understanding of the problem, even though data suggest that participants recognized the distinctiveness of the non-standard version compared to the standard one, deciding significantly more to stay on the non-standard version. Additionally, no differences were found in participants' confidence in their answers between the standard and non-standard versions of the task. There was also no difference in confidence ratings regarding accuracy in either version. A significant difference in confidence ratings in the standard version based on answer accuracy was found only in the condition with an explanation. Participants who provided the correct answer were significantly more confident in their response. The results of this research imply that explaining the problem leads to a better superficial understanding and improved performance on similar problems. Furthermore, this study could serve as a guideline for further research, suggesting that knowledge transfer is possible even at deeper levels of processing.