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Ch. 3 - Probability
Larson - Elementary Statistics: Picturing the World 8th Edition
Larson8th EditionElementary Statistics: Picturing the WorldISBN: 9780137493470Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoLarson 8th EditionCh. 3 - ProbabilityProblema 3.3.25b
Capitolo 3, Problema 3.3.25b

25. Working from Home The table shows the results of a survey that asked 1811 people how often they work from home. A person is selected at random from the sample. Find the probability of each event.
b. The person is female or does not work from home.
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Step 1: Identify the total number of people surveyed, which is given as 1811. This will be the denominator for calculating probabilities.
Step 2: Determine the total number of females from the table. The total number of females is 727. This represents one part of the event 'female or does not work from home.'
Step 3: Determine the total number of people who do not work from home. From the table, the total number of people who do not work from home is 753. This represents the other part of the event 'female or does not work from home.'
Step 4: Use the formula for the probability of 'A or B' (union of two events): \( P(A \cup B) = P(A) + P(B) - P(A \cap B) \). Here, A is 'female' and B is 'does not work from home.'
Step 5: Calculate \( P(A \cap B) \), the probability of a person being female and not working from home. From the table, the number of females who do not work from home is 312. Use this value to adjust the union probability calculation.

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Probability

Probability is a measure of the likelihood that an event will occur, expressed as a number between 0 and 1. In this context, it involves calculating the chance of selecting a person who is either female or does not work from home from the total sample. Understanding how to compute probabilities using the total number of favorable outcomes divided by the total number of possible outcomes is essential.
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Introduction to Probability

Union of Events

The union of events refers to the occurrence of at least one of the events in question. In this case, we are interested in the event where a person is either female or does not work from home. The probability of the union can be calculated using the formula P(A ∪ B) = P(A) + P(B) - P(A ∩ B), which accounts for any overlap between the two events.
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Probability of Multiple Independent Events

Complementary Events

Complementary events are pairs of outcomes where one event occurs if and only if the other does not. In this scenario, understanding the complement of the event 'does not work from home' can simplify calculations. For instance, if we know the probability of working from home, we can easily find the probability of not working from home by subtracting from 1.
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Complementary Events
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