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 5
![### Geometry Angle Problems
**Problem Description:**
Given the following angles:
- \( m∠ATB = 20° \)
- \( m∠BTD = 72° \)
- \( m∠CTD = 38° \)
Find the angle \( m∠ATC \).
**Diagram Explanation:**
The diagram shows four rays emanating from a common vertex \( T \). These rays are labeled as follows:
- Ray \( TA \)
- Ray \( TB \)
- Ray \( TC \)
- Ray \( TD \)
The points where the angles are formed between these rays are labeled appropriately to show the pairs of adjacent angles:
- Angle \( ATB \) is the angle between rays \( TA \) and \( TB \)
- Angle \( BTD \) is the angle between rays \( TB \) and \( TD \)
- Angle \( CTD \) is the angle between rays \( TC \) and \( TD \)
**Multiple Choice Options:**
The possible angles for \( m∠ATC \) are given as:
- A. \( 34° \)
- B. \( 52° \)
- C. \( 54° \)
- D. \( 58° \)
**Question:**
Calculate the value of \( m∠ATC \) based on the given angles.
**Solution Steps:**
1. Identify and sum up the angles around point \( T \).
2. Given that the sum of angles around a point is \( 360° \):
\[ m∠ATC = 360° - (m∠ATB + m∠BTD + m∠CTD) \]
3. Substitute the given values:
\[ m∠ATC = 360° - (20° + 72° + 38°) \]
4. Perform the calculation:
\[ m∠ATC = 360° - 130° \]
\[ m∠ATC = 230° \]
5. Therefore, \( m∠ATC = 230° \) is obtained. However, since the problem asks for a value within the range of the options provided and defined within the context of angles between rays, reevaluate in terms of the possible interpretation errors. Let's explore reevaluating:
Since calculating around \( T \):
The sum might be interpreted wrongly. Reevaluate it correctly, then directly solve based on](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc14456c8-c349-46c2-a794-2f6de4965e41%2Fe67d8ddb-28c1-4c39-b0ff-15d3a1a916b4%2Fpxtpwg_processed.png&w=3840&q=75)
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