A teacher was analyzing the relationship between students that received high scores on test and students that are involved in at least one extracurricular activity at school. The teacher surveyed all of their students. For
the students, 80% received high scores on tests, 60% were involved in at least one extracurricular activity, and
40% received high scores on tests and were involved in at least one extracurricular activity. Define events T
as a student that received high scores on tests and E represent a student is involved in at least one
extracurricular activity.
a) What is the probability a student receives high scores on tests and is not involved in at least one
extracurricular activity? Be sure to include a symbolic representation of the question.
b) What does P(E|T) represent in context? Find the value of P(E|T).