Answer to Question #273858 in Statistics and Probability for Miah

Question

In a certain Algebra 2 class of 26 students, 10 of them play basketball and 5 of

them play baseball. There are 3 students who play both sports. What is the

probability that a student chosen randomly from the class plays basketball or

baseball?

Answer 1

Let

A - a student playing basketball

B - a student playing baseball

Then

$P(A) = \frac{{10}}{{26}};\,\,P(B) = \frac{5}{{26}};\,\,P(A \cap B) = \frac{3}{{26}}$

So, the wanted probability is

$P(A \cup B) = P(A) + P(B) - P(A \cap B) = \frac{{10 + 5 - 3}}{{26}} = \frac{6}{{13}}$

Answer: $\frac{6}{{13}}$