in a certain algebra 2 class of 24 students, 16 of them play basketball and 10 of them play baseball. there…

in a certain algebra 2 class of 24 students, 16 of them play basketball and 10 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

in a certain algebra 2 class of 24 students, 16 of them play basketball and 10 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

Answer

Explanation:

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

$P(A\cup B)=P(A)+P(B)-P(A\cap B)$

Step2: Calculate $P(A)$, $P(B)$ and $P(A\cap B)$

$P(A)=\frac{16}{24}$, $P(B)=\frac{10}{24}$, $P(A\cap B)=\frac{7}{24}$

Step3: Substitute values into the formula

$P(A\cup B)=\frac{16}{24}+\frac{10}{24}-\frac{7}{24}=\frac{16 + 10-7}{24}=\frac{19}{24}$

Answer:

$\frac{19}{24}$