38. Getting to Work According to a survey, the probability that a randomly selected worker primarily rides a bicycle to work is 0.792. The probability that a randomly selected worker primarily takes public transportation to work is 0.071. (a) What is the probability that a randomly selected worker primarily rides a bicycle or takes public transportation to work?
Table of contents
- 1. Intro to Stats and Collecting Data1h 14m
- 2. Describing Data with Tables and Graphs1h 55m
- 3. Describing Data Numerically2h 5m
- 4. Probability2h 16m
- 5. Binomial Distribution & Discrete Random Variables3h 6m
- 6. Normal Distribution and Continuous Random Variables2h 11m
- 7. Sampling Distributions & Confidence Intervals: Mean3h 23m
- Sampling Distribution of the Sample Mean and Central Limit Theorem19m
- Distribution of Sample Mean - Excel23m
- Introduction to Confidence Intervals15m
- Confidence Intervals for Population Mean1h 18m
- Determining the Minimum Sample Size Required12m
- Finding Probabilities and T Critical Values - Excel28m
- Confidence Intervals for Population Means - Excel25m
- 8. Sampling Distributions & Confidence Intervals: Proportion1h 25m
- 9. Hypothesis Testing for One Sample3h 57m
- 10. Hypothesis Testing for Two Samples4h 50m
- Two Proportions1h 13m
- Two Proportions Hypothesis Test - Excel28m
- Two Means - Unknown, Unequal Variance1h 3m
- Two Means - Unknown Variances Hypothesis Test - Excel12m
- Two Means - Unknown, Equal Variance15m
- Two Means - Unknown, Equal Variances Hypothesis Test - Excel9m
- Two Means - Known Variance12m
- Two Means - Sigma Known Hypothesis Test - Excel21m
- Two Means - Matched Pairs (Dependent Samples)42m
- Matched Pairs Hypothesis Test - Excel12m
- 11. Correlation1h 24m
- 12. Regression1h 50m
- 13. Chi-Square Tests & Goodness of Fit2h 21m
- 14. ANOVA1h 57m
4. Probability
Addition Rule
Problem 6.1.17f
Textbook Question
[NW] [DATA] TelevisionsIn the Sullivan Statistics Survey I, individuals were asked to disclose the number of televisions in their household. In the following probability distribution, the random variable X represents the number of televisions in households.

f. What is the probability that a randomly selected household owns either three or four televisions?
Verified step by step guidance1
Identify the random variable X, which represents the number of televisions in a household, and the corresponding probabilities P(x) from the given probability distribution table.
Understand that the problem asks for the probability that a household owns either 3 or 4 televisions, which means we need to find P(X = 3 or X = 4).
Recall that for mutually exclusive events, the probability of either event occurring is the sum of their individual probabilities. So, we use the formula: \(P(X=3 \text{ or } X=4) = P(X=3) + P(X=4)\).
From the table, find the values of \(P(X=3)\) and \(P(X=4)\), which are 0.176 and 0.186 respectively.
Add these probabilities together to get the total probability: \(P(X=3 \text{ or } X=4) = 0.176 + 0.186\).
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Probability Distribution
A probability distribution lists all possible values of a random variable along with their associated probabilities. The sum of all probabilities must equal 1. It helps in understanding how likely different outcomes are in a random experiment.
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Calculating Probabilities in a Binomial Distribution
Random Variable
A random variable is a numerical outcome of a random phenomenon. In this case, X represents the number of televisions in a household. It can take on discrete values, each with a specific probability.
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Intro to Random Variables & Probability Distributions
Addition Rule of Probability
The addition rule states that the probability of either event A or event B occurring is the sum of their individual probabilities, provided the events are mutually exclusive. Here, to find the probability of owning three or four televisions, add P(3) and P(4).
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