Under the circumstances described, the type of fraud most likely to occur is skimming. Skimming involves stealing cash before it is recorded on the organization's books. Since receipts were issued only upon request and the inventory manager had control over collecting and depositing payments, there is an opportunity for undetected theft of cash payments.References: Common types of fraud in cash handling environments, as outlined in fraud detection and prevention resources by the IIA.

An effective risk management process is indicated by the organization's ability to identify and adequately assess significant risks. This involves understanding the full range of potential risks the organization faces and evaluating their magnitude and likelihood in a way that aligns with the organization's risk appetite and capacity. This ability ensures that strategic decisions are informed and that risks are managed proactively.
References: COSO Framework on Enterprise Risk Management, which outlines the importance of identifying and assessing risks in relation to an organization's objectives.

The use of due professional care by the internal audit activity is best demonstrated by internal auditors undertaking the necessary training to complete their audit work. Due professional care involves applying the diligence and judgment needed to conduct audits effectively. This includes continuous training and development to ensure auditors are proficient in their field and up-to-date with relevant audit standards, technologies, and methodologies, which aligns with the International Standards for the Professional Practice of Internal Auditing from the Institute of Internal Auditors (IIA).References: The Institute of Internal Auditors (IIA) - International Standards for the Professional Practice of Internal Auditing

The best description of the board's role in establishing effective organizational governance is that the board has oversight responsibility for organizational resources. This includes overseeing how resources are allocated and managed, ensuring that the organization's governance framework is effective, and monitoring overall organizational performance to align with strategic objectives.References: Governance frameworks and the role of boards in corporate governance.

The most appropriate action for the Chief Audit Executive (CAE) to take in the scenario where staff might mistakenly believe the new internal auditor is related to the procurement manager is to discuss the matter with the appropriate personnel to alleviate concerns. This action ensures that concerns about independence and objectivity are addressed transparently, maintaining trust in the internal audit function.References: The IIA's Code of Ethics and standards on objectivity, which stress the importance of maintaining and demonstrating impartiality in all audit engagements.