le below displays results from experiments with polygraph instruments. Find P(subject lied negative test result). Compare this result with the probability of selecting a subject with a negative test result, given that the e P(subject lied negative test result) and P(negative test result subject lied) equal? Did the Subject Actually Lie? No (Did Not Lie) Yes (Lied) sitive test results 10 44 egative test results 12 34 Pisubject lied | negative test result) = (Round to three decimal places as needed.) Find the probability of selecting a subject with a negative test result, given that the subject lied. P(negative test result | subject lied) = (Round to three decimal places as needed) Compare the two values Are they equal? No O Yes
Addition Rule of Probability
It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.
Expected Value
When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).
Probability Distributions
Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.
Basic Probability
The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.
![**Polygraph Instrument Results**
The table below displays results from experiments with polygraph instruments. Analyze the conditional probabilities from the data provided.
### Table: Polygraph Test Results
| Did the Subject Actually Lie? | No (Did Not Lie) | Yes (Lied) |
|-------------------------------|------------------|------------|
| Positive test results | 10 | 44 |
| Negative test results | 34 | 12 |
### Questions
1. **Find \( P(\text{subject lied } | \text{ negative test result}) \)**
- Calculate the probability that a subject lied given that they received a negative test result.
- Round your answer to three decimal places as needed.
\[
P(\text{subject lied } | \text{ negative test result}) = \left(\frac{\text{Number of subjects who lied and got a negative test result}}{\text{Total number of subjects who got a negative test result}}\right)
\]
2. **Find \( P(\text{negative test result } | \text{ subject lied}) \)**
- Calculate the probability of a negative test result given that the subject lied.
- Round your answer to three decimal places as needed.
\[
P(\text{negative test result } | \text{ subject lied}) = \left(\frac{\text{Number of subjects who lied and got a negative test result}}{\text{Total number of subjects who lied}}\right)
\]
3. **Compare the Two Values**
- Are the two calculated probabilities equal?
- Options:
- No
- Yes
Select the appropriate answer.
*(Ensure to calculate based on the table values to complete the exercise accurately.)*](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff619d33a-1cef-47db-a949-758134183c85%2F810d89b3-2e0d-42d8-8018-b1851e33db59%2Fovrl6gni_processed.jpeg&w=3840&q=75)
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