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Ch. 3 - Probability
Larson - Elementary Statistics: Picturing the World 8th Edition
Larson8th EditionElementary Statistics: Picturing the WorldISBN: 9780137493470Not the one you use?Change textbook
All textbooksLarson 8th EditionCh. 3 - ProbabilityProblem 3.1.21
Chapter 3, Problem 3.1.21

Finding the Probability of an Event In Exercises 21-24, the probability that an event will not happen is given. Find the probability that the event will happen. 
21. P(E') =0.95

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1
Step 1: Understand the problem. The probability of an event not happening, denoted as P(E'), is given as 0.95. You are tasked with finding the probability of the event happening, denoted as P(E).
Step 2: Recall the relationship between the probability of an event happening and not happening. The sum of these probabilities must equal 1, as they are complementary events. Mathematically, this is expressed as: P(E) + P(E') = 1.
Step 3: Rearrange the formula to solve for P(E). Subtract P(E') from both sides: P(E) = 1 - P(E').
Step 4: Substitute the given value of P(E') into the formula. In this case, P(E') = 0.95, so the equation becomes: P(E) = 1 - 0.95.
Step 5: Perform the subtraction to find the probability of the event happening. This will give you the value of P(E).

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Complementary Events

In probability theory, complementary events are two outcomes of a single event that cannot occur at the same time. If an event E occurs, its complement E' (not E) represents all outcomes where E does not happen. The sum of the probabilities of an event and its complement is always equal to 1, which is a fundamental principle in probability.
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Probability Calculation

Probability is a measure of the likelihood that an event will occur, expressed as a number between 0 and 1. To find the probability of an event happening, you can subtract the probability of the event not happening from 1. For example, if P(E') = 0.95, then P(E) = 1 - P(E') = 0.05, indicating a low likelihood of the event occurring.
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Basic Probability Rules

Basic probability rules include the addition and multiplication rules, which help in calculating the probabilities of combined events. The addition rule states that the probability of either of two mutually exclusive events occurring is the sum of their individual probabilities. Understanding these rules is essential for solving more complex probability problems and for interpreting results correctly.
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Related Practice
Textbook Question

Classifying Types of Probability In Exercises 53-58, classify the statement as an example of classical probability, empirical probability, or subjective probability. Explain your reasoning.

55. An analyst feels that the probability of a team winning an upcoming game is 60%.

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Textbook Question

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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.

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Textbook Question

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Textbook Question

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Textbook Question

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