In the diagram below, XS and YR intersect at Z. Segments XY and RS are drawn perpendicular to Y R to form triangles XYZ and SRZ. Y S. Which statement is always true? O A. AXY Z A SRZ O B. XY SR YZ RZ O C. (XY)(SR) = (XZ)(RZ) %3D O D. XS YR
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.
Question 6
![### Diagram and Problem Statement:
In the diagram below, \( \overline{XS} \) and \( \overline{YR} \) intersect at \( Z \). Segments \( XY \) and \( RS \) are drawn perpendicular to \( \overline{YR} \) to form triangles \( XYZ \) and \( SRZ \).
\[
\begin{array}{c}
X\\
|\backslash \\
| \ \backslash Z \\
| \ \ \ \ \backslash \\
|_____Y \ \ \ \ \ \ \ \ R \\
| \ \ \ \ \ \ \ backslash \\
|_____ \ \_\ \ R \ S \\
\end{array}
\]
### Multiple-Choice Question:
Which statement is always true?
#### Options:
- **A.** \( \triangle XYZ \cong \triangle SRZ \)
- **B.** \( \frac{XY}{SR} \cong \frac{YZ}{RZ} \) ⬤ (This option is marked)
- **C.** \( (XY)(SR) = (XZ)(RZ) \)
- **D.** \( \overline{XS} \cong \overline{YR} \)
### Explanation of Diagram and Choices:
In the diagram provided, segment \( XY \) is perpendicular to \( \overline{YR} \), forming a right angle at \( Y \). Similarly, segment \( RS \) is perpendicular to \( \overline{YR} \), forming a right angle at \( S \). This arrangement forms two right triangles: \( \triangle XYZ \) and \( \triangle SRZ \).
#### Analysis of the Options:
- **Option A:** Suggests that \( \triangle XYZ \cong \triangle SRZ \), meaning the triangles are congruent in all aspects. This would require all corresponding sides and angles to be equal, which is not necessarily evident from the given information.
- **Option B:** Suggests that the ratios of the corresponding sides of the triangles are equal, indicating similarity rather than congruence, and this is a common result in right triangles sharing an altitude from the right angle to the hypotenuse. This option is marked as correct in the image.
- **Option C:** Suggests a relationship involving the product of sides of the triangles, indicative of certain](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffeb8ca9d-9969-400c-8a44-95370ebd76d8%2F406e42f5-5d5c-4f98-bad9-6f939fda8075%2F80boleg_processed.png&w=3840&q=75)
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