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91Ó°ÊÓ

Express the indicated degree of likelihood as a probability value between 0 and \(1 .\) When making a random guess for an answer to a multiple choice question on an SAT test, the possible answers are \(\mathrm{a}, \mathrm{b}, \mathrm{c}, \mathrm{d}, \mathrm{e}\), so there is 1 chance in 5 of being correct.

Short Answer

Expert verified
The probability is 0.2.

Step by step solution

01

Understand the Problem

The task is to express the probability of a random guess being correct on a multiple choice question with five possible answers (a, b, c, d, e). The probability value must be between 0 and 1.
02

Identify the Total Number of Outcomes

There are 5 possible answers (a, b, c, d, e) for the multiple choice question.
03

Identify the Successful Outcome

A successful outcome is guessing the correct answer. There is exactly 1 correct answer out of the 5 possible answers.
04

Calculate the Probability

The probability of a random guess being correct is calculated by dividing the number of successful outcomes by the total number of outcomes: \[ P(\text{correct guess}) = \frac{1 \text{ successful outcome}}{5 \text{ total outcomes}} = \frac{1}{5} \]
05

Express the Probability as a Decimal

Convert the fraction to a decimal: \[ P(\text{correct guess}) = \frac{1}{5} = 0.2 \]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

multiple choice probability
When faced with multiple choice questions, especially in exams like the SAT, understanding how to compute probability can be very helpful. Each answer option on a multiple choice question represents an individual outcome.
If there are five options, such as a, b, c, d, e, each option has an equal chance of being selected. This total number of choices is key to finding the probability of picking the correct one.
Only one of these options will be correct.
Therefore, the probability of selecting the correct answer is calculated as the ratio of one successful outcome over the total number of outcomes. The formula used here is: \[ P(\text{correct guess}) = \frac{1}{\text{total number of choices}} \]
This basic understanding forms the foundation of grasping probability in multiple choice settings.By understanding how each option contributes to the total outcomes, you can start making more informed guesses in multiple choice examinations.
calculating probability
To calculate probability, you need to know two things: the number of successful outcomes and the total number of outcomes. This can be expressed as a fraction: \[ P(\text{event}) = \frac{\text{number of successful outcomes}}{\text{total number of outcomes}} \].
In our SAT multiple choice question example, there are 5 possible outcomes (a, b, c, d, e). Only one of these outcomes is a correct answer.
So, the probability of guessing the right answer is: \[ P(\text{correct guess}) = \frac{1}{5} = 0.2 \].
When you convert the fraction into a decimal, it makes it easier to visualize the likelihood. Hence, a random guess gives you a 0.2 (or 20%) chance of getting it right.
Mastering this simple calculation can help you understand more complex probability problems down the road.
SAT test probability
Probability plays a significant role in standardized tests like the SAT. Each question on the test typically comprises multiple choice questions. Understanding the probability can help in making educated guesses.
Let's focus on improving your guessing strategy for SAT questions.
If you don't know the answer, and if there is no penalty for guessing wrongly (as in some test formats), you can calculate your chances of success by understanding the number of options available.
In this example, there are 5 choices per question. So, even a random guess has a success rate of 20%.
However, employing probability to eliminate obviously wrong answers can increase your chances.
For instance, if you can eliminate two incorrect answers, then you have 3 choices left, making your success rate: \[ P(\text{correct guess}) = \frac{1}{3} \]
Which means a roughly 33.3% chance of getting it right.
Thus, understanding how to calculate and use probabilities can give you a slight edge in approaches, especially under exam settings.

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Most popular questions from this chapter

Express all probabilities as fractions. In a horse race, a quinela bet is won if you selected the two horses that finish first and second, and they can be selected in any order. The 140 th running of the Kentucky Derby had a field of 19 horses. What is the probability of winning a quinela bet if random horse selections are made?

Composite Water Samples The Fairfield County Department of Public Health tests water for the presence of \(E\). coli (Escherichia coli) bacteria. To reduce laboratory costs, water samples from 10 public swimming areas are combined for one test, and further testing is done only if the combined sample tests positive. Based on past results, there is a \(0.005\) probability of finding \(E\). coli bacteria in a public swimming area. Find the probability that a combined sample from 10 public swimming areas will reveal the presence of \(E\). coli bacteria. Is that probability low enough so that further testing of the individual samples is rarely necessary?

Find the indicated complements. A U.S. Cellular survey of smartphone users showed that \(26 \%\) of respondents answered "yes" when asked if abbreviations (such as LOL) are annoying when texting. What is the probability of randomly selecting a smartphone user and getting a response other than "yes"?

Let \(A=\) the event of getting at least 1 defective iPhone when 3 iPhones are randomly selected with replacement from a batch. If \(5 \%\) of the iPhones in a batch are defective and the other \(95 \%\) are all good, which of the following are correct? a. \(P(\bar{A})=(0.95)(0.95)(0.95)=0.857\) b. \(P(A)=1-(0.95)(0.95)(0.95)=0.143\) c. \(P(A)=(0.05)(0.05)(0.05)=0.000125\)

What does the symbol ! represent? Six different people can stand in a line \(6 !\) different ways, so what is the actual number of ways that six people can stand in a line?

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