A test for marijuana usage was tried on 173173 subjects who did not use marijuana. The test result was wrong 6767 times.
a. Based on the available​ results, find the probability of a wrong test result for a person who does not use marijuana.
b. Is it​ "unlikely" for the test to be wrong for those not using​ marijuana?
Consider an event to be unlikely if its probability is less than or equal to 0.05.

Let's solve each part of the problem step by step.

### Part (a): Probability of a Wrong Test Result
To find the probability of a wrong test result for a person who does not use marijuana, we use the formula:

\[
\text{Probability} = \frac{\text{Number of wrong test results}}{\text{Total number of subjects}}
\]

Given:
- Number of wrong test results = 6767
- Total number of subjects = 173173

\[
\text{Probability} = \frac{6767}{173173}
\]

Let's calculate this.

\[
\text{Probability} = \frac{6767}{173173} \approx 0.0391
\]

### Part (b): Is it "Unlikely" for the Test to be Wrong?
An event is considered "unlikely" if its probability is less than or equal to 0.05.

The probability we calculated is approximately 0.0391.

Since \(0.0391 \leq 0.05\), the event is considered "unlikely."

### Summary:
- **(a)** The probability of a wrong test result for a person who does not use marijuana is approximately 0.0391.
- **(b)** Yes, it is "unlikely" for the test to be wrong for those not using marijuana, as the probability is less than or equal to 0.05.

Would you like further details on these calculations or have any questions?

Here are some related questions for further exploration:
1. How does the sample size affect the probability of a wrong test result?
2. What is the probability of the test being correct for a person who does not use marijuana?
3. How would the probability change if the number of wrong test results increased or decreased?
4. What is the importance of understanding the concept of "unlikely" in probability?
5. Can this probability be used to assess the reliability of the marijuana test in general?

**Tip:** Understanding probability thresholds, like the 0.05 level for "unlikely" events, is crucial in statistics, especially when making decisions based on uncertain outcomes.

Explore the probability of a wrong test result for individuals who do not use marijuana. Learn how to calculate probability using real-world data and understand the significance of probability thresholds in statistical analysis.

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