MATHEMATICS · Multi-part · CBSE · Mathematics · Probability · Probability
Problem
In a college, students may choose to play football, and they must also undergo a compulsory physical fitness test.
(i) It is known that 18% of the students both play football and pass the fitness test. Given that 90% of football players pass the fitness test, find the percentage of students who play football.
(ii) The overall probability that a student passes the fitness test is 0.4. Find the probability that a student passes the fitness test given that the student does not play football.
(iii) Are the events “the student plays football” and “the student passes the fitness test” independent? Justify your answer with calculation.