Textbook Question
39. You are given that P(A) = 0.15 and P(B) = 0.40. Do you have enough information to find P(A or B)? Explain.
4. Probability
Addition Rule
2:51 minutesProblem 3.3.22b
Textbook Question
22. Brexit A survey asked 1115 British adults how Britain's decision to leave the European Union has impacted the country. The results are shown in the Pareto chart. Find the
probability of each event. (Adapted from Ipsos)
b. Randomly selecting a British adult who feels that the move has had a very negative impact on Great Britain
Verified step by step guidance1
Step 1: Identify the total number of respondents in the survey. According to the problem, the total number of British adults surveyed is 1115.
Step 2: Locate the number of respondents who feel that the move has had a 'very negative' impact. From the Pareto chart, this value is 256.
Step 3: Recall the formula for probability: \( P(A) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \). Here, the favorable outcome is the number of respondents who feel the impact is 'very negative', and the total number of outcomes is the total number of respondents.
Step 4: Substitute the values into the formula: \( P(\text{Very Negative}) = \frac{256}{1115} \).
Step 5: Simplify the fraction if necessary to express the probability in its simplest form or as a decimal.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Probability
Probability is a measure of the likelihood that a particular event will occur, expressed as a number between 0 and 1. In this context, it refers to the chance of randomly selecting a British adult who perceives the impact of Brexit as 'very negative.' This can be calculated by dividing the number of respondents who selected 'very negative' by the total number of respondents.
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Pareto Chart
A Pareto chart is a type of bar graph that represents the frequency or impact of problems in a descending order. It helps to visualize the most significant factors in a dataset. In this case, the chart displays the responses of British adults regarding the impact of Brexit, allowing for easy identification of the most common perceptions.
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Survey Sampling
Survey sampling involves selecting a subset of individuals from a larger population to gather insights about that population. In this scenario, 1,115 British adults were surveyed to understand their views on Brexit. The sample size is crucial for ensuring that the results are representative and can be generalized to the broader population.
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