A person commits an offense concerning a deadly weapon in a penal institution if, while confined, he intentionally,________, or recklessly carries a deadly weapon.

The correct choice is "knowingly" because this term is specifically defined in criminal law as being aware of one’s conduct and the circumstances surrounding it. In the context of a penal institution, an individual can be considered to have committed an offense concerning a deadly weapon if they carry it intentionally, knowingly, or recklessly. The use of "knowingly" indicates that the person was aware that they were carrying a deadly weapon while confined, which fulfills an essential element of the offense as it demonstrates a level of awareness and intentionality.

The other options do not align with the legal definitions and required mental states recognized in criminal law. "Carelessly" implies a lack of attention but does not meet the threshold of knowledge regarding the action. "Innocently" suggests that the individual is unaware of their actions, which would not constitute an offense. "Secretively" implies a hidden action but does not necessarily indicate awareness of having a deadly weapon or the implications of that act in a penal institution setting. Therefore, "knowingly" is the most appropriate term that captures the necessary mental state required for this offense.