In a survey conducted in a college, it was found that 40% of the students prefer studying in the library, 30% prefer studying in their dorm rooms, and 20% prefer studying in both the library and their dorm rooms.What is the probability that a randomly selected student does not study either in the library or in their dorm room?
Question
In a survey conducted in a college, it was found that 40% of the students prefer studying in the library, 30% prefer studying in their dorm rooms, and 20% prefer studying in both the library and their dorm rooms.What is the probability that a randomly selected student does not study either in the library or in their dorm room?
Solution
To solve this problem, we first need to understand that the total probability of all possible outcomes is always 1 (or 100%). In this case, the possible outcomes are studying in the library, studying in the dorm room, studying in both places, or studying in neither.
From the survey, we know that:
- 40% of students prefer studying in the library
- 30% of students prefer studying in their dorm rooms
- 20% of students prefer studying in both the library and their dorm rooms
We can add these percentages together to find the total percentage of students who study in either the library, their dorm rooms, or both.
40% (library) + 30% (dorm rooms) + 20% (both) = 90%
Since the total probability must be 100%, and we know that 90% of students study in either the library, their dorm rooms, or both, we can subtract this from 100% to find the percentage of students who study in neither the library nor their dorm rooms.
100% - 90% = 10%
Therefore, the probability that a randomly selected student does not study either in the library or in their dorm room is 10%.
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