Question

A teacher was analyzing the relationship between students that received high scores on tests 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 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).

Answer 1

a) The probability a student receives high scores on tests and is not involved in at least one extracurricular activity is 0.4 or 40%. b) P(E|T) represents the conditional probability that a student is involved in at least one extracurricular activity given that they received high scores on tests. The value of P(E|T) is 0.5 or 50%.

Step-by-step explanation:

a) The probability a student receives high scores on tests and is not involved in at least one extracurricular activity can be represented as P(T and not E). The formula for calculating this probability is P(T and not E) = P(T) - P(T and E). From the given information, we know that P(T) = 0.8 and P(T and E) = 0.4. Therefore, P(T and not E) = 0.8 - 0.4 = 0.4, or 40%.

b) P(E|T) represents the conditional probability that a student is involved in at least one extracurricular activity given that they received high scores on tests. The formula for calculating this probability is P(E|T) = P(T and E) / P(T). From the given information, we know that P(T and E) = 0.4 and P(T) = 0.8. Therefore, P(E|T) = (0.4 / 0.8) = 0.5, or 50%.