in a certain algebra 2 class of 27 students, 15 of them play basketball and 17 of them play baseball. there…

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?

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

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 $P(A\cap B)$

$P(A)=\frac{15}{27}$, $P(B)=\frac{17}{27}$, $P(A\cap B)=\frac{7}{27}$

Step3: Substitute values into the formula

$P(A\cup B)=\frac{15}{27}+\frac{17}{27}-\frac{7}{27}=\frac{15 + 17- 7}{27}=\frac{25}{27}$

Answer:

$\frac{25}{27}$