Math Problem Statement
Solution
The image appears to contain a probability question related to drug testing. The company is testing 1200 applicants, and 35% of the applicants have used drugs. The question asks how many applicants who have done drugs will not get caught, assuming the testing facility is 95% accurate.
Let’s break this down:
- 1200 applicants in total.
- 35% have done drugs, so the number of applicants who have used drugs is:
Now, to find how many of the drug users will not get caught:
- The testing facility has 95% accuracy, meaning there is a 5% chance of error.
- Assuming the test is 95% accurate in detecting drug use, 5% of the drug users will not be caught.
Therefore, 21 applicants who have used drugs will not get caught.
Would you like more details on any part of this problem, or would you like to explore related questions?
Here are some related questions:
- What would be the result if the testing accuracy were lower, say 90%?
- How would the outcome change if the percentage of drug users were 50% instead of 35%?
- What is the probability that a clean applicant (non-drug user) gets falsely identified as a drug user?
- How do you calculate the number of applicants who will be caught, given the accuracy of the test?
- If the test had a 99% accuracy rate, how many of the 420 drug users would not get caught?
Tip: To approach probability problems involving testing accuracy, always break the situation down into known percentages and apply them directly to the numbers provided.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Probability
Percentages
Statistics
Formulas
Number of drug users = Total applicants × Percentage of drug users
False negatives = Number of drug users × (1 - Accuracy of test)
Theorems
Basic Probability Theory
Suitable Grade Level
Grades 9-12
Related Recommendation
Probability Problem: Drug Test Results and Conditional Probability
Probability of False Positives: Binomial and Normal Approximation in Drug Test Analysis
Calculating Probabilities from a Drug Test Contingency Table
Marijuana Drug Test: Calculating False Positives and Negatives
Calculate Probability of False Positive in Pre-Employment Drug Screening