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In a certain Algebra 2 class of 26 students, 17 of them play basketball and 21 of them play baseball. There are 15 students who play both sports. What is the probability that a student chosen randomly from the class plays basketball or baseball? Answer:

In a certain Algebra 22 class of 2626 students, 1717 of them play basketball and 2121 of them play baseball. There are 1515 students who play both sports. What is the probability that a student chosen randomly from the class plays basketball or baseball?\newlineAnswer:

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Q. In a certain Algebra 22 class of 2626 students, 1717 of them play basketball and 2121 of them play baseball. There are 1515 students who play both sports. What is the probability that a student chosen randomly from the class plays basketball or baseball?\newlineAnswer:
  1. Principle of Inclusion-Exclusion: To find the probability that a student chosen randomly from the class plays basketball or baseball, we need to use the principle of inclusion-exclusion. This principle states that for any two sets, the size of their union is the size of the first set plus the size of the second set minus the size of their intersection.
  2. Given Information: First, let's identify the given information:\newline- Total number of students in the class: 2626\newline- Number of students who play basketball: 1717\newline- Number of students who play baseball: 2121\newline- Number of students who play both sports: 1515
  3. Calculate Students Playing Either Sport: Using the principle of inclusion-exclusion, we calculate the number of students who play either basketball or baseball (or both) as follows:\newlineNumber of students who play basketball or baseball == Number of students who play basketball ++ Number of students who play baseball −- Number of students who play both sports
  4. Plug in Numbers: Now, let's plug in the numbers:\newlineNumber of students who play basketball or baseball = 17+21−1517 + 21 - 15
  5. Perform Calculation: Perform the calculation:\newlineNumber of students who play basketball or baseball = 38−1538 - 15
  6. Continue Calculation: Continue the calculation:\newlineNumber of students who play basketball or baseball = 2323
  7. Calculate Probability: To find the probability, we divide the number of students who play basketball or baseball by the total number of students in the class:\newlineProbability = Number of students who play basketball or baseballTotal number of students\frac{\text{Number of students who play basketball or baseball}}{\text{Total number of students}}
  8. Express Probability: Now, let's calculate the probability: Probability = 2326\frac{23}{26}
  9. Express Probability: Now, let's calculate the probability:\newlineProbability = 2326\frac{23}{26}To express the probability in simplest form, we can leave it as a fraction or convert it to a decimal:\newlineProbability = 2326≈0.8846\frac{23}{26} \approx 0.8846

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