Standard Tests Standard tests, such as the SAT or ACT or MCAT, tend to make extensive use of multiple-choice questions because they are easy to grade using software. If one such multiple choice question has possible correct answers of a, b, c, d, e, what is the probability of a wrong answer if the answer is a random guess?
Table of contents
- 1. Intro to Stats and Collecting Data55m
- 2. Describing Data with Tables and Graphs1h 55m
- 3. Describing Data Numerically1h 45m
- 4. Probability2h 16m
- 5. Binomial Distribution & Discrete Random Variables2h 33m
- 6. Normal Distribution and Continuous Random Variables1h 38m
- 7. Sampling Distributions & Confidence Intervals: Mean1h 53m
- 8. Sampling Distributions & Confidence Intervals: Proportion1h 12m
- 9. Hypothesis Testing for One Sample2h 19m
- 10. Hypothesis Testing for Two Samples3h 22m
- 11. Correlation1h 6m
- 12. Regression1h 4m
- 13. Chi-Square Tests & Goodness of Fit1h 20m
- 14. ANOVA1h 0m
4. Probability
Complements
Problem 3.1.19
Textbook Question
Finding the Probability of the Complement of an Event In Exercises 17-20, the probability that an event will happen is given. Find the probability that the event will not happen.
19. P(E)=0.03

1
Step 1: Understand the concept of the complement of an event. The complement of an event E, denoted as E', represents all outcomes in the sample space that are not part of event E. The sum of the probabilities of an event and its complement is always equal to 1.
Step 2: Recall the formula for the probability of the complement of an event: \( P(E') = 1 - P(E) \). This formula is derived from the fact that \( P(E) + P(E') = 1 \).
Step 3: Identify the given probability of the event \( P(E) \). In this problem, \( P(E) = 0.03 \).
Step 4: Substitute the given value of \( P(E) \) into the formula for \( P(E') \): \( P(E') = 1 - 0.03 \).
Step 5: Simplify the expression to find \( P(E') \). This will give you the probability that the event will not happen.

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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Probability of an Event
Probability quantifies the likelihood of an event occurring, expressed as a number between 0 and 1. A probability of 0 indicates impossibility, while a probability of 1 indicates certainty. In this case, P(E) = 0.03 means there is a 3% chance that event E will occur.
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Complement of an Event
The complement of an event refers to all outcomes in which the event does not occur. It is denoted as P(E') and can be calculated using the formula P(E') = 1 - P(E). This concept is essential for determining the probability of an event not happening based on the probability of it happening.
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Calculating Complement Probability
To find the probability of the complement of an event, subtract the probability of the event from 1. For example, if P(E) = 0.03, then P(E') = 1 - 0.03 = 0.97. This means there is a 97% chance that event E will not occur, illustrating how to effectively use the complement rule in probability.
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