Let's solve this step by step: ### **Step 1: Identify the numbers needed** We need to find the probability that the subject lied, **given that the test yields a positive result** (positive predictive value). From the table: - Positive test results & Did Not Lie: **14** - Positive test results & Lied: **42** So, total positive test results = **14 + 42 = 56** Number who lied (and got positive result) = **42** **Explanation:** We are focusing only on the cases where the test result was positive. --- ### **Step 2: Set up the probability formula** We want \( P(\text{Lied} \mid \text{Positive result}) \). This is given by: \[ P(\text{Lied} \mid \text{Positive result}) = \frac{\text{Number who lied and got positive result}}{\text{Total number with positive result}} \] Plug in the numbers: \[ P(\text{Lied} \mid \text{Positive result}) = \frac{42}{56} \] **Explanation:** We use the definition of conditional probability for the positive predictive value. --- ### **Step 3: Calculate the probability** \[ \frac{42}{56} = 0.75 \] **Explanation:** Dividing 42 by 56 gives us 0.75. This should be rounded to three decimal places, but since it's already at two decimal places, it remains **0.750**. --- ## **Final Answer** The probability is **0.750**.