Police plan to enforce speed limits by using radar traps at four different locations within the city limits. The radar traps at each of the locations L1. Lz. La and La will he operated 40%, 20%, 30%, and 40% of the time. A person who is speeding on her way to work has probabilities of 0.2, 0.1, 0.5, and 0.2, respectively, of passing through these locations. If the person received a speeding ticket on her way to work, what is the probability that she passed through the radar trap loted at L,? If the person received a speeding ticket on her way to work, the probability that she passed through the radar trap located at L2 is (Type an integer or a simplified fraction.)

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### Probability of Receiving a Speeding Ticket

Police enforce speed limits by using radar traps at four different locations within the city limits. The radar traps at each of the locations \( L_1 \), \( L_2 \), \( L_3 \), and \( L_4 \) will be operated 40%, 20%, 30%, and 40% of the time. A person who is speeding on her way to work has probabilities of 0.2, 0.1, 0.5, and 0.2, respectively, of passing through these locations.

**Question:**
If the person received a speeding ticket on her way to work, what is the probability that she passed through the radar trap located at \( L_2 \)?

If the person received a speeding ticket on her way to work, the probability that she passed through the radar trap located at \( L_2 \) is:

*(Type an integer or a simplified fraction.)*

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Enter your answer in the answer box and then click Check Answer.

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### Explanation:
Given:
- Operation probabilities of radar traps at locations \( L_1 \), \( L_2 \), \( L_3 \), and \( L_4 \) are 0.4, 0.2, 0.3, and 0.4 respectively.
- Probability of the person passing through \( L_1 \), \( L_2 \), \( L_3 \), and \( L_4 \) are 0.2, 0.1, 0.5, and 0.2 respectively.

Use Bayes' Theorem to solve the problem.
Transcribed Image Text:### Probability of Receiving a Speeding Ticket Police enforce speed limits by using radar traps at four different locations within the city limits. The radar traps at each of the locations \( L_1 \), \( L_2 \), \( L_3 \), and \( L_4 \) will be operated 40%, 20%, 30%, and 40% of the time. A person who is speeding on her way to work has probabilities of 0.2, 0.1, 0.5, and 0.2, respectively, of passing through these locations. **Question:** If the person received a speeding ticket on her way to work, what is the probability that she passed through the radar trap located at \( L_2 \)? If the person received a speeding ticket on her way to work, the probability that she passed through the radar trap located at \( L_2 \) is: *(Type an integer or a simplified fraction.)* **Answer Box:** Enter your answer in the answer box and then click Check Answer. **Interface Elements:** - **All parts showing:** (A progress bar indicating completion status) - **Clear All:** (A button to clear entered data) - **Check Answer:** (A button to submit the entered answer) ### Explanation: Given: - Operation probabilities of radar traps at locations \( L_1 \), \( L_2 \), \( L_3 \), and \( L_4 \) are 0.4, 0.2, 0.3, and 0.4 respectively. - Probability of the person passing through \( L_1 \), \( L_2 \), \( L_3 \), and \( L_4 \) are 0.2, 0.1, 0.5, and 0.2 respectively. Use Bayes' Theorem to solve the problem.
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