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In a certain Algebra 2 class of 30 students, 15 of them play basketball and 16 of them play baseball. There are 7 students who play both sports. What is the probability that a student chosen randomly from the class plays basketball or baseball?

Question

In a certain Algebra 2 class of 30 students, 15 of them play basketball and 16 of them play baseball. There are 7 students who play both sports. What is the probability that a student chosen randomly from the class plays basketball or baseball?

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Solution

To solve this problem, we first need to understand that the question is asking for the probability that a student plays either basketball or baseball, which includes students who play both.

Step 1: Find the number of students who play either basketball or baseball.

This is not simply the sum of the basketball and baseball players, because that would count the 7 students who play both sports twice. So, we add the number of basketball players to the number of baseball players and subtract the number of students who play both:

15 (basketball players) + 16 (baseball players) - 7 (both sports) = 24 students

Step 2: Calculate the probability.

The probability of an event is calculated by dividing the number of favorable outcomes by the total number of outcomes. In this case, the favorable outcomes are the 24 students who play basketball or baseball, and the total outcomes are the 30 students in the class:

24 (either sport) / 30 (total students) = 0.8

So, the probability that a student chosen randomly from the class plays basketball or baseball is 0.8, or 80%.

This problem has been solved

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In a class of 30 students, 18 play basketball, 12 play soccer, and 8 play both basketball and soccer. How many students play only basketball?

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