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.
Only question 3
![## Finding the Lateral Area of Prisms
### Instructions:
Find the lateral area of each prism shown below.
### Prisms:
#### 1. Rectangular Prism
Dimensions:
- Height: 12 units
- Width: 12 units
- Length: 10 units
This prism is a standard three-dimensional rectangular box with specified height, width, and length.
#### 2. Rectangular Prism
Dimensions:
- Height: 6 units
- Width: 8 units
- Length: 12 units
This prism is another three-dimensional rectangular box with specified height, width, and length, though the dimensions differ from the first prism.
#### 3. Triangular Prism
Dimensions:
- Base of the triangular face: 5 units
- Height of the triangular face: 6 units
- Length of the prism: 10 units
- Other side of the triangular face: 8 units
This prism has a triangular base and extends to form a three-dimensional shape. The dimensions include the base, height, and the length of the prism, along with another side of the triangular face.
#### 4. Triangular Prism
Dimensions:
- Base of the triangular face: 9 units
- Height of the triangular face: 9 units
- Length of the prism: 12 units
- Other side of the triangular face: 9 units
Similar to the third prism, this has a triangular base but with larger dimensions for the base, height, and other side of the triangle.
### Explanation:
Lateral area refers to the sum of the areas of all the faces of a prism, excluding its two bases. To find the lateral area, calculate the area of each side face and add them together.
For rectangular prisms, the lateral area can be found by computing:
\[ \text{Lateral Area} = 2 \times (\text{Height} \times \text{Length}) + 2 \times (\text{Height} \times \text{Width}) \]
For triangular prisms, compute the lateral area by:
\[ \text{Lateral Area} = (\text{Perimeter of the triangular base}) \times (\text{Length of the prism}) \]
Note: The perimeter of the triangular base is the sum of all the edges of the triangle.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcb602927-d5c2-4b17-99bc-cf43c066f5a5%2F259e947e-3c4f-4f2e-9a92-2226d6796ea5%2F0r0fssb_processed.png&w=3840&q=75)
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