What is the Probability of Owning Either a Microwave or CD Player?

In summary, the probability that Joe owns either a microwave or a CD player, but not both, is 40%. This can be calculated by subtracting the probability that he owns both from the probabilities of owning each individually and then adding them together. A Venn diagram can also be used to visualize the probabilities.
  • #1
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Homework Statement



The probability that Joe owns a microwave oven is 75%; the probability that he owns a CD player is 45%; and the probability that he owns both is 40%. Find the probability that he owns either one but not both.

Homework Equations



(work posted below)

The Attempt at a Solution



P(only microwave)= .75-.4 = .35
P(only CD Player) = .45 - .4 = .05
P(only micr. or CD Pl) = .35 + .05 = .4

Answer = .4
 
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  • #2
You got it! Try visualizing it with a Venn diagram: 2 overlapping circles representing probabilities that he owns either or both, surrounded by a large circle that represents probability that he owns either, both, or neither. (Hint: probability he owns neither is 0.2)
 

1. What is the difference between statistics and probability?

Statistics is the study of collecting, analyzing, and interpreting data to make conclusions and predictions about a population. Probability is the study of the likelihood of events occurring based on mathematical principles.

2. How is probability used in statistics?

Probability is used in statistics to help make predictions and inferences about a population based on a sample. It allows us to calculate the likelihood of certain events occurring and make decisions based on that information.

3. What is the importance of understanding statistics and probability?

Understanding statistics and probability is crucial in making informed decisions and drawing accurate conclusions based on data. It also allows us to make predictions and assess risks in various situations.

4. What are some common misconceptions about statistics and probability?

Some common misconceptions about statistics and probability include thinking that a small sample size is representative of a larger population, assuming correlation implies causation, and believing that a low probability means something is impossible.

5. How can I improve my understanding and skills in statistics and probability?

To improve your understanding and skills in statistics and probability, it is important to practice solving problems and working with data. You can also take courses, attend workshops or seminars, and consult with experts in the field to gain more knowledge and experience.

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