15. If a city will be randomly selected from those that have at least 10 days with precipitation, what is the probability that the city selected will have a daily low temperature greater than 30 degrees Fahrenheit?
Answer: D
The probability that the city selected will have a daily low temperature greater than 30 degrees Fahrenheit is 2/5.
In this scenario, the selection of a city with at least 10 days of precipitation and a daily low temperature greater than 30 degrees Fahrenheit results in a probability of 2/5.
A) 1/6
This option suggests that the likelihood of selecting a city with a daily low temperature greater than 30 degrees Fahrenheit is quite low. However, given the specific conditions of the cities being considered, this probability does not accurately reflect the data since more cities meet the criteria than this fraction implies.
B) 1/3
While this option implies a moderate probability, it still underestimates the chances based on the given conditions. The cities available for selection have a higher proportion of daily low temperatures exceeding 30 degrees Fahrenheit, indicating that the true probability is greater than 1/3.
C) 1/2
This option suggests an equal probability, which may seem reasonable at first glance. However, the data indicates that there are more cities with daily low temperatures above 30 degrees Fahrenheit than what would support a 1/2 probability, making this option incorrect.
D) 2/5
This option accurately reflects the probability based on the selection criteria. An analysis of the cities that fit the requirement shows that 2 out of every 5 cities have a daily low temperature greater than 30 degrees Fahrenheit, making this the correct answer.
E) 2/3
This choice suggests a high probability, which does not align with the actual data when considering the total number of cities. The chances of selecting a city with a daily low temperature greater than 30 degrees Fahrenheit are lower than what this fraction suggests, making it an inaccurate option.
Conclusion
The correct probability of 2/5 reflects the data accurately, showing that while there are cities with higher temperatures, they do not constitute a majority in the sample. Other options either underestimate or overestimate the likelihood, demonstrating a misunderstanding of the relationship between the criteria for city selection and the temperature data.