in a certain algebra 2 class of 29 students, 5 of them play basketball and 19 of them play baseball. there…

Answer:

$\frac{2}{29}$

Explanation:

Step1: Find number of students who play at least one sport

$29 - 7=22$

Step2: Use the inclusion - exclusion principle

Let $A$ be the set of basketball players and $B$ be the set of baseball players. We know $n(A) = 5$, $n(B)=19$ and $n(A\cup B)=22$. By the formula $n(A\cup B)=n(A)+n(B)-n(A\cap B)$, we can find $n(A\cap B)$. $n(A\cap B)=n(A)+n(B)-n(A\cup B)$ $n(A\cap B)=5 + 19-22$ $n(A\cap B)=2$

Step3: Calculate the probability

The probability $P$ that a randomly chosen student plays both sports is $\frac{n(A\cap B)}{n(\text{total})}$. Since $n(A\cap B) = 2$ and $n(\text{total})=29$, $P=\frac{2}{29}$