ocld 4.) You are a campaign manager assigned to a fairly conservative rural district, where 65.3% of registered voters are in the Republican party. You hire a new pollster to gather some opinion data. In her report, she indicated that she interviewed twenty-six randomly selected voters, all of whom were Republican. What is the probability that all of the interviewees were Republican? Would you believe her? Why or why not? P/Z6
Compound Probability
Compound probability can be defined as the probability of the two events which are independent. It can be defined as the multiplication of the probability of two events that are not dependent.
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Probability theory is a branch of mathematics that deals with the subject of probability. Although there are many different concepts of probability, probability theory expresses the definition mathematically through a series of axioms. Usually, these axioms express probability in terms of a probability space, which assigns a measure with values ranging from 0 to 1 to a set of outcomes known as the sample space. An event is a subset of these outcomes that is described.
Conditional Probability
By definition, the term probability is expressed as a part of mathematics where the chance of an event that may either occur or not is evaluated and expressed in numerical terms. The range of the value within which probability can be expressed is between 0 and 1. The higher the chance of an event occurring, the closer is its value to be 1. If the probability of an event is 1, it means that the event will happen under all considered circumstances. Similarly, if the probability is exactly 0, then no matter the situation, the event will never occur.
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1. **What is the probability that they all have group B and blood type Rh- blood?**
\[
\left(\frac{2}{100}\right) \times \left(\frac{2}{99}\right) \times \left(\frac{2}{98}\right) = \frac{1}{121275} = 8.245722538 \times 10^{-6} = 0.000008 \, \text{(rounded)}
\]
*(Note: It seems there is a consideration of whether there should be a multiplication by another factor \(a = 0\).)*
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4. **Scenario:**
You are a campaign manager assigned to a fairly conservative rural district, where 65.3% of registered voters are in the Republican party. You hire a new pollster to gather some opinion data. In her report, she indicated that she interviewed 26 randomly selected voters, all of whom were Republican.
**Question:** What is the probability that all of the interviewees were Republican? Would you believe her? Why or why not?
\[
P\left(\frac{26}{4652}\right) = 39.58946232377 = 39.59\%
\]
**Explanation:**
- Out of 4652 voters, 26 were Republicans, leading to a probability of 39.59%. This result is notably lower than the expected 65.3%, suggesting skepticism regarding the accuracy of the pollster's report, implying the likelihood exceeds typical expectations.
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5. **Scenario:**
Seven wayward students decided to spend the sunny afternoon at the beautiful Olana estate instead of going to statistics, unfortunately forgetting they had a major exam. They concoct a story, claiming that all commute together in a minivan and they had a flat tire. The professor agrees to give them a makeup exam, on the provision that they all attend his office separately for the exam and cannot discuss it with each other afterwards. When they each arrive in turn to take the exam, they find that it consists of a single question, “Which tire was flat?”
**Question:** What is the probability that the duplicitous students would pass the exam?
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This content showcases practical applications of probability in real-life scenarios, enhancing understanding and critical analysis of statistical data.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F636db579-c98b-49b6-abb1-a55c8bad6b2a%2F38d93efd-96f7-4f96-bf24-c6e21d8c56e7%2Fiq7f78b.jpeg&w=3840&q=75)
We’ll answer the first question since the exact one wasn’t specified.
Please submit a new question specifying the one you’d like answered.
Let us assume X= number of Republican
n=sample size= 26
p=probability of getting a Republican= 65.3%=0.653
Each interviewee is independent of the other interviewees.
So, X follows a normal distribution with n=26 and p=0.653
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