The contingency table below shows the results of a survey of video viewing habits by age video Viewdng Pletfore Preferred Viewer Age 18-34 35-54 55+ Column Total Mobile/Laptop Device TV Screen 39 Row Total 35 74 16 3. 46 10 54 100 Find the following probabilities or percentages (a) Probability that a viewer is aged 18-34. (Round your answer to 2 decimel places.) Probability (b) Probability that a viewer prefers watching videos on a TV screen. (Round your enswer to 2 decim Probability (c) Percentage of viewers who are 18-34 and prefer videos on e mobile or laptop device. Percentage of viewers
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.
![**Video Viewing Habits by Age - Educational Resource**
The contingency table presented below displays the results of a survey examining video viewing habits by age group. The table specifies the number of individuals within three distinct age groups and their preferred video viewing platform (either Mobile/Laptop Device or TV Screen).
| Viewer Age | Video Viewing Platform Preferred | | Row Total |
|------------|----------------------------------|--------|------------|
| | Mobile/Laptop Device | TV Screen | |
| 18-34 | 35 | 5 | 40 |
| 35-54 | 3 | 39 | 42 |
| 55+ | 8 | 90 | 98 |
| **Column Total** | **46** | **54** | **180** |
### Questions and Calculations
1. **(a) Probability that a viewer is aged 18–34.**
- **Calculation**:
\[
\text{Probability} = \frac{\text{Number of viewers aged 18-34}}{\text{Total number of viewers}} = \frac{40}{180} \approx 0.22
\]
- **Answer (Rounded to 2 decimal places)**:
\[
0.22
\]
2. **(b) Probability that a viewer prefers watching videos on a TV screen.**
- **Calculation**:
\[
\text{Probability} = \frac{\text{Number of viewers preferring TV screens}}{\text{Total number of viewers}} = \frac{54}{180} \approx 0.30
\]
- **Answer (Rounded to 2 decimal places)**:
\[
0.30
\]
3. **(c) Percentage of viewers who are 18–34 and prefer videos on a mobile or laptop device.**
- **Calculation**:
\[
\text{Percentage} = \left( \frac{\text{Number of viewers aged 18-34 preferring Mobile/Laptop}}{\text{Total number of viewers}} \right) \times 100 = \left( \frac{35}{180} \right) \times 100 \approx 19.44\%
\]
- **Answer**:
\[
19](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa0697825-11e3-404a-a16a-b66263def85b%2Fa3ac357b-24af-49eb-9fe5-b909219f21a8%2Fdy72dce.jpeg&w=3840&q=75)
Step by step
Solved in 2 steps with 1 images
