To determine the detection risk that the auditors plan to use for planning the remainder of the audit work, we need to understand the relationship between the assessed risk of material misstatement, the risk of failing to express a correct opinion, and the planned level of detection risk.
The risk of failing to express a correct opinion is composed of two components: the assessed risk of material misstatement and the planned level of detection risk. These two components are inversely related. As the assessed risk of material misstatement increases, the planned level of detection risk decreases, and vice versa.
In this case, the assessed risk of material misstatement is given as 0.50, and the auditors want to achieve a risk of failing to express a correct opinion of 0.05. To reach this desired risk level, the auditors would need to set their planned level of detection risk at 0.05.
Therefore, the correct answer is 0.05.