In a survey, 52.5% of respondents have portable earbuds and 30% of the respondents who have portable earbuds also have a smart speaker. What is the probability that a respondent has both portable earbuds and a smart speaker? If necessary, round to the nearest hundredth of a percent.Probability: %
Question
In a survey, 52.5% of respondents have portable earbuds and 30% of the respondents who have portable earbuds also have a smart speaker. What is the probability that a respondent has both portable earbuds and a smart speaker? If necessary, round to the nearest hundredth of a percent.Probability: %
Solution
To find the probability that a respondent has both portable earbuds and a smart speaker, we need to multiply the probability of having portable earbuds by the probability of having a smart speaker given that the respondent has portable earbuds.
- Convert the percentages to decimals: 52.5% becomes 0.525 and 30% becomes 0.30.
- Multiply these two probabilities together: 0.525 * 0.30 = 0.1575.
- Convert this decimal back to a percentage by multiplying by 100: 0.1575 * 100 = 15.75%.
So, the probability that a respondent has both portable earbuds and a smart speaker is approximately 15.75%.
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