Use the following data for problem 1. It represents the results of 300 patients with depression treated with

Anti-depressant Talk Therapy No treatment Total

Improved 80 52 75 207

No improvement 20 48 25 93

100 100 100 300

1.a What is P(improved)?

1.b What is P(talk therapy)?

1.c What is P(improved|talk therapy)?

1.d What is P(improved and talk therapy)?

1.e What is P(improved or talk therapy)?

2. Assume that the probability that a college student has a laptop is 0.3 and that the probability that a college student has a STEM major is 0.40. Also assume that the probability that a college student both has a laptop and is a STEM major is 0.20. Are having a laptop and having a STEM major independent events?