Question

question
in a certain algebra 2 class of 27 students, 15 of them play basketball and 17 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?
answer attempt 1 out of 2
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Explanation:

Step1: Use the formula for \(P(A\cup B)\)

The formula for the probability of the union of two events \(A\) and \(B\) is \(P(A\cup B)=P(A)+P(B)-P(A\cap B)\). Here, \(n(A) = 15\) (number of basketball - players), \(n(B)=17\) (number of baseball - players), \(n(A\cap B) = 7\) (number of students who play both), and \(n(S)=27\) (total number of students).
\(P(A)=\frac{n(A)}{n(S)}\), \(P(B)=\frac{n(B)}{n(S)}\), \(P(A\cap B)=\frac{n(A\cap B)}{n(S)}\)

Step2: Substitute the values

\(P(A\cup B)=\frac{15 + 17-7}{27}\)
First, calculate the numerator: \(15+17 - 7=25\)
So, \(P(A\cup B)=\frac{25}{27}\)

Answer:

\(\frac{25}{27}\)