in a certain algebra 2 class of 20 students, 5 of them play basketball and 6 of them play baseball. there…

in a certain algebra 2 class of 20 students, 5 of them play basketball and 6 of them play baseball. there are 2 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 20 students, 5 of them play basketball and 6 of them play baseball. there are 2 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 $P(A\cap B)$

$P(A)=\frac{5}{20}$, $P(B)=\frac{6}{20}$, $P(A\cap B)=\frac{2}{20}$

Step3: Substitute values into the formula

$P(A\cup B)=\frac{5}{20}+\frac{6}{20}-\frac{2}{20}=\frac{5 + 6- 2}{20}=\frac{9}{20}$

Answer:

$\frac{9}{20}$