Compound Probability
Compound probability can be defined as the probability of the two events which are independent. It can be defined as the multiplication of the probability of two events that are not dependent.
Tree diagram
Probability theory is a branch of mathematics that deals with the subject of probability. Although there are many different concepts of probability, probability theory expresses the definition mathematically through a series of axioms. Usually, these axioms express probability in terms of a probability space, which assigns a measure with values ranging from 0 to 1 to a set of outcomes known as the sample space. An event is a subset of these outcomes that is described.
Conditional Probability
By definition, the term probability is expressed as a part of mathematics where the chance of an event that may either occur or not is evaluated and expressed in numerical terms. The range of the value within which probability can be expressed is between 0 and 1. The higher the chance of an event occurring, the closer is its value to be 1. If the probability of an event is 1, it means that the event will happen under all considered circumstances. Similarly, if the probability is exactly 0, then no matter the situation, the event will never occur.
![**Angle Calculation in Trigonometry**
**Problem Statement:**
Solve for \( x \). Round to the nearest tenth of a degree, if necessary.
**Figure Description:**
The diagram depicts a triangle \( QRS \):
- \( Q \) is the vertex where the right angle is located.
- \( \overline{QS} \) is opposite the angle \( x \).
- \( \overline{RQ} \) is adjacent to the angle \( x \).
- \( \overline{RS} \) is the hypotenuse of the triangle.
- The lengths of the sides are:
- \( \overline{RQ} = 84 \) units
- \( \overline{RS} = 98 \) units
To find \( x \), we can use trigonometric ratios. Specifically, we will use the tangent (tan) function, which is defined as the ratio of the opposite side to the adjacent side in a right-angled triangle. The formula is:
\[ \tan(x) = \frac{\text{Opposite Side}}{\text{Adjacent Side}} \]
Given:
- The opposite side \( \overline{QS} = 84 \) units
- The adjacent side \( \overline{RQ} = 98 \) units
We calculate:
\[ \tan(x) = \frac{84}{98} \]
By using the arctangent (inverse tangent) to find \( x \):
\[ x = \arctan\left(\frac{84}{98}\right) \]
Use a calculator to solve:
\[ x \approx 40.6^\circ \]
Thus:
\[ x \approx 40.6^\circ \] rounded to the nearest tenth of a degree.
This value may be used in the context of various educational materials or practical applications requiring trigonometric solutions.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb223a19b-0fd0-443c-881a-6f762159fad5%2Feecf9696-dab5-4765-9225-d82dfb79e17f%2Fqd6veu_processed.jpeg&w=3840&q=75)
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