Question

this venn diagram shows sports played by 10 students.
let event a = the student plays basketball.
let event b = the student plays soccer.
what is ( p(a \text{ or } b) )?

a. ( \frac{3}{5} )
b. ( \frac{2}{5} )
c. ( \frac{1}{10} )
d. partially visible

(venn diagram details: mai, karl, jada, gabby outside; fran, ian, juan in plays basketball only; ella in both plays basketball and plays soccer; mickey, marcus in plays soccer only)

Explanation:

Answer:

To find \( P(A \text{ or } B) \), we use the principle of inclusion - exclusion for probability: \( P(A \cup B)=P(A)+P(B)-P(A \cap B) \)

1. First, determine the number of students in each set:

• Total number of students \( n = 10 \)
• Students who play basketball (event \( A \)): Fran, Ian, Juan, Ella. So \( n(A)=4 \)
• Students who play soccer (event \( B \)): Ella, Mickey, Marcus. So \( n(B) = 3\)
• Students who play both basketball and soccer (event \( A\cap B \)): Ella. So \( n(A\cap B)=1 \)

1. Calculate the number of students who play either basketball or soccer (\( n(A\cup B) \)):

Using the formula \( n(A\cup B)=n(A)+n(B)-n(A\cap B) \)
\( n(A\cup B)=4 + 3-1=6 \)

1. Calculate the probability \( P(A\cup B) \):

\( P(A\cup B)=\frac{n(A\cup B)}{n}=\frac{6}{10}=\frac{3}{5} \)

So the answer is A. \(\frac{3}{5}\)