in a certain algebra 2 class of 30 students, 25 of them play basketball and 15 of them play baseball. there…

in a certain algebra 2 class of 30 students, 25 of them play basketball and 15 of them play baseball. there are 12 students who play both sports. what is the probability that a student chosen randomly from the class plays basketball or baseball?

in a certain algebra 2 class of 30 students, 25 of them play basketball and 15 of them play baseball. there are 12 students who play both sports. what is the probability that a student chosen randomly from the class plays basketball or baseball?

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 $P(A\cap B)$

$P(A)=\frac{25}{30}$, $P(B)=\frac{15}{30}$, $P(A\cap B)=\frac{12}{30}$

Step3: Substitute values into the formula

$P(A\cup B)=\frac{25}{30}+\frac{15}{30}-\frac{12}{30}=\frac{25 + 15- 12}{30}=\frac{28}{30}=\frac{14}{15}$

Answer:

$\frac{14}{15}$