Final answer:
A group member who neglects their part in a project, pushing their responsibilities onto others without contributing, is demonstrating a 4. Saboteur role, akin to the free rider problem. This behavior is detrimental and hampers the group's collective effort towards achieving its goals.
Step-by-step explanation:
A group member who says "why don't you just take care of this; I'm too busy and have better things to do than work on this group project" is not taking a constructive role in the group dynamics. Instead of performing as a leader, follower, or observer, this individual is displaying the tendencies of a 4) Saboteur.
The behavior suggests a lack of interest in contributing to the group's success and is akin to the free rider problem where individuals gain the benefit without contributing to the group's goal, which can lead to project stagnation or failure.
The laissez-faire leadership style is one where the leader provides autonomy to team members to make their own decisions. However, in this case, the lack of contribution is more indicative of a member who is derailing the group effort rather than leading it or allowing others to work independently.
In summary, the scenario presented does not align with a healthy group dynamic. Such an attitude can impact the group's ability to achieve goals collectively, as each member's contribution is instrumental in the success of the whole.