The governor of the state of Maryland, Martin O'Malley, ran for re-election in November, 2010. Before the election, from September 22-26, 2010, the Washington Post conducted a poll in which respondents were asked: "lf the election for Maryland governor were held today, for whom would you vote?" In an article summarizing the results of the poll, Washington Post journalists reported that "A total of 1,448 randomly selected adults in Maryland were interviewed, including... 730 voters likely to cast ballots." The sample was intended to represent the population of likely Maryland voters at that time period in September, 2010. The article summarized the responses of the likely voters using the following categories: "for Governor Martin O'Malley", "for Bob Ehrlich", and "for Other/no opinion".
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.
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![### Analysis of 2010 Maryland Gubernatorial Poll Results
#### Poll Overview
Before the 2010 gubernatorial election in Maryland, a poll was conducted from September 22–26 by the Washington Post. The poll sampled voters to determine their preference if the governor election were held at that time.
#### Methodology
- **Sample Size:** 1,448 randomly selected adults in Maryland.
- **Likely Voters:** Out of the total sample, 730 were identified as likely voters.
Respondents were asked, “If the election for Maryland governor were held today, for whom would you vote?” The poll provided three response categories:
1. For Governor Martin O'Malley
2. For Bob Ehrlich
3. For Other/No opinion
#### Poll Results
The following is a likely tally of the responses from the 730 likely voters:
- **For Governor Martin O'Malley:** 382 responses
- **For Bob Ehrlich:** 302 responses
- **For Other/No opinion:** 46 responses
#### Statistical Analysis
To verify if there is a significant difference in the distribution of voter preferences as compared to previous polling data, a Chi-square goodness-of-fit test was performed. Previous polls suggested the following expected distributions:
- **O'Malley:** 48%
- **Ehrlich:** 46%
- **Other/No opinion:** 6%
#### Calculation Summary
1. **Observed Frequencies:**
- **O'Malley:** 382
- **Ehrlich:** 302
- **Other/No opinion:** 46
2. **Expected Frequencies (based on earlier percentage data):**
- **O'Malley:** 730 × 0.48 = 350.4
- **Ehrlich:** 730 × 0.46 = 335.8
- **Other/No opinion:** 730 × 0.06 = 43.8
3. **Chi-square Calculation:**
\[ χ^2 = \sum \frac{{(O - E)^2}}{E} \]
- O'Malley: \[ \frac{{(382 - 350.4)^2}}{350.4} = 2.850 \]
- Ehrlich: \[ \frac{{(302 - 335.8)^2}}{335.8} = 3.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8261e31d-85d7-419e-b7db-b3889750b80d%2Fdb5b9de6-dadf-4ad2-8354-3f265f1ca444%2Fl8yubgj_reoriented.jpeg&w=3840&q=75)
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