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.)

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.)

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Concept explainers

Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!

Question

### 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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### 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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