Question

In a certain Algebra 2 class of 30 students, 12 of them play basketball and 17 of them
play baseball. There are 5 students who play neither sport. What is the probability
that a student chosen randomly from the class plays both basketball and baseball?

Answer 1

Answer:

The probability of students playing both basketball and baseball = $\frac{2}{15}$

Step-by-step explanation:

Total strength of class = 30 students

Number of students who play basketball = 12

Number of students who play baseball = 17

Number of students who play neither sport = 5

Number of students that play either sport = $30-5$ = 25

Number of students who play both sports will be given as:

⇒ Number of students playing basketball + Number of students playing baseball - Number of students playing either

⇒ $12+17-25$

⇒ $4$

Thus probability of students playing both basketball and baseball is given as:

⇒ $\frac{Number\ of\ students\ playing\ both}{Total\ number\ of\ students}$

⇒ $\frac{4}{30}$

Dividing numerator and denominator by 2 to reduce to simplest fraction.

⇒ $\frac{4\div 2}{30\div 2}$

⇒ $\frac{2}{15}$ (Answer)