In a particular college class, 60% of the students are women. Fifty percent of all students in the class have long hair. Forty-five percent of the students are women and have long hair. Of the women students, 75% have long hair. Let W be the event that a student is a women. Let L be the event that a student has long hair. One student is picked randomly. Are the events of being a woman and having long hair independent?
- The following probabilities are given in this example:
- P(W) = 0.60; P(L) = 0.50
- P(W AND L) = 0.45
- P(L|W) = 0.75
The choice you make depends on the information you have. You could use the first or last condition on the list for this example. You do not know P(W|L) yet, so you cannot use the second condition.
OpenStax Introductory Statistics 2e, 3.2 Independent and Mutually Exclusive Events, exercise 15