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 1
![**Directions**: Solve each problem. Your answer may be rounded to the nearest hundredth if necessary. Make sure your work includes the formula you are using and the measurements for each variable.
### 1) Find the area.
An irregular quadrilateral is depicted with the following measurements:
- One side of the shape is 11 meters long.
- The height perpendicular to the 11-meter side from the opposite vertex is 5 meters.
- One of the angles formed by the height and the side is 60 degrees.
### 2) Find the area.
A parallelogram is depicted with the following characteristics:
- Two of the sides are marked with a length of 12 units.
- The angle between these two sides is 60 degrees.
- The height perpendicular to one of the sides forms a right angle (90 degrees) and is indicated for calculation purposes.
For both shapes, to find the area you will use different formulas based on the geometry.
**For the first shape (trapezoid/irregular quadrilateral)**:
- Recognize that the given dimensions and angle can be used to find the base and height of a simpler geometric shape, such as a parallelogram.
- The area \( A \) of a trapezoid can be found using:
\[
A = \text{Base} \times \text{Height}
\]
Substitute the given dimensions:
\[
A = 11 \, \text{m} \times 5 \, \text{m} = 55 \, \text{m}^2
\]
**For the second shape (parallelogram)**:
- The area \( A \) of a parallelogram can be given by the formula:
\[
A = \text{Base} \times \text{Height}
\]
- The base is 12 units and the height is derived using trigonometric relationships with the height and the angle. If \( b \) is the base and \( h \) is the height:
\[
h = 12 \sin(60^\circ)
\]
Thus, you will use:
\[
A = 12 \times (12 \sin(60^\circ))
\]
\[
\sin(60^\circ) = \frac{\sqrt{3}}{2}
\]
\[
A = 12](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7acfa03c-ce8c-4cd5-a52f-d1ef747591d8%2Fe595dc96-d0cb-4d4c-8a69-cd610f9774fe%2Fbec89r_processed.png&w=3840&q=75)
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