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In a certain Algebra 2 class of 24 students, 9 of them play basketball and 5 of them play baseball. There are 3 students who play both sports. What is the probability that a student chosen randomly from the class plays basketball or baseball?

In a certain Algebra 22 class of 2424 students, 99 of them play basketball and 55 of them play baseball. There are 33 students who play both sports. What is the probability that a student chosen randomly from the class plays basketball or baseball?

Full solution

Q. In a certain Algebra 22 class of 2424 students, 99 of them play basketball and 55 of them play baseball. There are 33 students who play both sports. What is the probability that a student chosen randomly from the class plays basketball or baseball?
  1. Calculate Total Students: Determine the total number of students who play either basketball or baseball.\newlineTo find the number of students who play either basketball or baseball, we add the number of students who play basketball to the number of students who play baseball and then subtract the number of students who play both sports to avoid double-counting.\newlineNumber of students playing basketball or baseball = Number of basketball players + Number of baseball players - Number of students playing both sports\newlineCalculation: 99 (basketball players) + 55 (baseball players) - 33 (both sports) = 1111
  2. Find Probability: Calculate the probability that a student plays basketball or baseball.\newlineThe probability is the number of students playing either sport divided by the total number of students in the class.\newlineProbability = Number of students playing basketball or baseballTotal number of students\frac{\text{Number of students playing basketball or baseball}}{\text{Total number of students}}\newlineCalculation: 1124\frac{11}{24}