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In a class of 23 students, 8 play an instrument and 13 play a sport. There are 4 students who do not play an instrument or a sport. What is the probability that a student who plays an instrument does not play a sport? Answer:

In a class of 2323 students, 88 play an instrument and 1313 play a sport. There are 44 students who do not play an instrument or a sport. What is the probability that a student who plays an instrument does not play a sport?\newlineAnswer:

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Q. In a class of 2323 students, 88 play an instrument and 1313 play a sport. There are 44 students who do not play an instrument or a sport. What is the probability that a student who plays an instrument does not play a sport?\newlineAnswer:
  1. Calculate Total Students: First, let's determine the total number of students who play an instrument or a sport, or both. We know that 44 students do not play either, so the number of students who play at least one is the total number of students minus those who play neither.\newlineCalculation: 2323 students (total) - 44 students (neither) = 1919 students (at least one).
  2. Find Students Playing Both: Next, we need to find out how many students play only an instrument. We know that 88 play an instrument and 1313 play a sport, but this information includes students who might play both. Since there are 1919 students who play at least one, and 44 who play neither, we can find the number of students who play both an instrument and a sport by subtracting the number of students who play at least one from the sum of students who play an instrument and those who play a sport.\newlineCalculation: $(\(8\) \text{ students (instrument)} + \(13\) \text{ students (sport)}) - \(19\) \text{ students (at least one)} = \(2\) \text{ students (both)}.
  3. Calculate Students Playing Only: Now we can calculate the number of students who play only an instrument by subtracting the number of students who play both an instrument and a sport from the total number of students who play an instrument.\(\newline\)Calculation: \(8\) students (instrument) - \(2\) students (both) = \(6\) students (only instrument).
  4. Calculate Probability: To find the probability that a student who plays an instrument does not play a sport, we divide the number of students who play only an instrument by the total number of students who play an instrument.\(\newline\)Calculation: \(6\) students (only instrument) / \(8\) students (instrument) = \(\frac{3}{4}\).

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