Math Problem Statement

A company is interviewing 1200 applicants. They send all the applicants to get drug tested at a facility that is 95% accurate. 35% of the applicants have actually done some form of drugs in the testable time frame, but the rest are clean. How many of the applicants that have done drugs will not get caught?

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: 1200×0.35=420 applicants.1200 \times 0.35 = 420 \text{ applicants}.

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. 420×0.05=21 applicants.420 \times 0.05 = 21 \text{ applicants}.

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:

  1. What would be the result if the testing accuracy were lower, say 90%?
  2. How would the outcome change if the percentage of drug users were 50% instead of 35%?
  3. What is the probability that a clean applicant (non-drug user) gets falsely identified as a drug user?
  4. How do you calculate the number of applicants who will be caught, given the accuracy of the test?
  5. 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.

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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