Question

there are 200 students in the 8th grade class at alleghany middle school. of these students, 8% play basketball and 14% play soccer. six students play on both teams. what is the probability that a student plays either basketball or soccer?
a. 19%
b. 22%
c. 25%
d. 16%

Explanation:

Step1: Calculate the number of basketball players

The number of basketball players is \(8\%\) of \(200\), which is \(0.08\times200 = 16\) students.

Step2: Calculate the number of soccer players

The number of soccer players is \(14\%\) of \(200\), which is \(0.14\times200=28\) students.

Step3: Use the formula \(n(A\cup B)=n(A)+n(B)-n(A\cap B)\)

Here, \(n(A)\) (basketball) \( = 16\), \(n(B)\) (soccer) \( = 28\), \(n(A\cap B)=6\). So \(n(A\cup B)=16 + 28-6=38\) students.

Step4: Calculate the probability

The probability \(P=\frac{38}{200}=0.19 = 19\%\)

Answer:

A. 19%