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In a certain Algebra 2 class of 25 students, 5 of them play basketball and 14 of them play baseball. There are 8 students who play neither sport. What is the probability that a student chosen randomly from the class plays both basketball and baseball? Answer:

In a certain Algebra 22 class of 2525 students, 55 of them play basketball and 1414 of them play baseball. There are 88 students who play neither sport. What is the probability that a student chosen randomly from the class plays both basketball and baseball?\newlineAnswer:

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Q. In a certain Algebra 22 class of 2525 students, 55 of them play basketball and 1414 of them play baseball. There are 88 students who play neither sport. What is the probability that a student chosen randomly from the class plays both basketball and baseball?\newlineAnswer:
  1. Given Information: Let's denote the total number of students in the class as TT, the number of students who play basketball as BB, the number of students who play baseball as BaBa, and the number of students who play neither sport as NN. We are given the following:\newlineT=25T = 25 (total students)\newlineB=5B = 5 (students who play basketball)\newlineBa=14Ba = 14 (students who play baseball)\newlineN=8N = 8 (students who play neither sport)\newlineWe need to find the number of students who play both basketball and baseball, which we'll denote as BBaBBa.
  2. Find Students Playing at Least One Sport: First, we can find the number of students who play at least one sport by subtracting the number of students who play neither sport from the total number of students:\newlineStudents who play at least one sport = T−NT - N\newlineStudents who play at least one sport = 25−825 - 8\newlineStudents who play at least one sport = 1717
  3. Use of Inclusion-Exclusion Principle: Next, we can use the principle of inclusion-exclusion to find the number of students who play both sports. The principle of inclusion-exclusion states that for any two sets, the number of elements in either set is equal to the sum of the number of elements in each set minus the number of elements in both sets. In terms of probability:\newlineNumber of students who play both sports BBaBB_a = Number of students who play basketball BB + Number of students who play baseball BaBa - Number of students who play at least one sport\newlineBBa=B+Ba−(Students who play at least one sport)BB_a = B + Ba - (\text{Students who play at least one sport})\newlineBBa=5+14−17BB_a = 5 + 14 - 17\newlineBBa=19−17BB_a = 19 - 17\newlineBBa=2BB_a = 2
  4. Calculate Probability: Now that we have the number of students who play both basketball and baseball, we can find the probability that a randomly chosen student from the class plays both sports. The probability is the number of students who play both sports divided by the total number of students:\newlineProbability PP = BBaT\frac{BBa}{T}\newlineP=225P = \frac{2}{25}

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