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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.
![**Title: Understanding Composite Figures**
**Introduction:**
Composite figures arise in various geometry problems and are typically composed of more than one basic shape. In this lesson, we will analyze a figure composed of a rectangle and a semicircle.
**Figure Explanation:**
The image depicts a composite figure consisting of:
1. A rectangle.
2. A semicircle positioned on top of the rectangle.
**Dimensions:**
- The rectangle has a height of \(5\) units and a length of \(12\) units.
- The semicircle is formed on the top length of the rectangle with a diameter equal to the length of the rectangle, \(12\) units, which makes the radius \(6\) units (since the radius is half of the diameter).
**Step-by-Step Guide to Find the Area of the Composite Figure:**
1. **Area of the Rectangle:**
\[
A_{\text{rectangle}} = \text{length} \times \text{height} = 12 \times 5 = 60 \text{ square units}
\]
2. **Area of the Semicircle:**
The area of a full circle with radius \(r\) is given by:
\[
A_{\text{circle}} = \pi r^2
\]
Since we have a semicircle (half of a circle), the area will be:
\[
A_{\text{semicircle}} = \frac{1}{2} \pi r^2
\]
Substituting \(r = 6\) units:
\[
A_{\text{semicircle}} = \frac{1}{2} \pi (6)^2 = \frac{1}{2} \pi (36) = 18 \pi \text{ square units}
\]
3. **Total Area of the Composite Figure:**
\[
A_{\text{total}} = A_{\text{rectangle}} + A_{\text{semicircle}} = 60 + 18\pi \text{ square units}
\]
**Conclusion:**
The composite figure's total area combines the area of the rectangle and the semicircle. Comprehending how to decompose and calculate the areas of these basic shapes forms the foundation for solving more complex geometrical problems.
Feel free to review the detailed breakdown if you need further clarification on any steps!
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