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.