1. Which of the following pair of events are independent? A) Event I: You sleep late. Event II: You are late for class. B) Event I: You write proper thank-you notes. Event II: You get invited back. C) Event I: The first time you flip a coin, you get head. Event II: The second time you flip a coin, you get tail. D) Event I: General Electric stock goes up. Event II: General Motors stocks goes up.

2. If P (B) = 1/4, P (A B) = 1/2 and P (A|B) = 2/3, then which of the following statements is true? A) P (A) = 1/3 B) P (A B) = 1/12 C) P (B|A) = 1/5 D) A and B are not independent.

3. In a certain community, 28% of the houses have fireplaces and 51% have garages. Consider a randomly selected house in the community. Is the probability that it has either a fireplace or a garage equal to 28% + 51% = 79%? Explain briefly why or why not.

4. (2 points) According to the National Health Statistics Reports, 16% of American women have one child, and 21% have two children. For a randomly selected American woman, is the probability that she has either one or two children equal to 16% + 21% = 37%? Explain briefly why or why not.

5. (6 points) Jiang always drinks coffee after arriving at Posvar Hall in the morning, while Marla and Tara sometimes join her. The probability that Marla drinks coffee with Jiang is 1/4 and the probability that Tara drinks coffee with Jiang is 3/8. The probability that Jiang drinks coffee by herself is 1/2. (a) (2 points) What is the probability that Jiang has coffee with both Marla and Tara? (b) (2 points) If Tara did not have coffee with Jiang, what is the probability that Marla was not there either? (e) (2 points) If Jiang had coffee with Marla this morning, what is the probability that Tara did not join them? (Hint: You want to start off by considering this question: given the information provided in the story what those numbers are really about?), which of the two analytical tools we have covered in class will be more helpful to solve this problem, a probability table or a probability tree? )

6. You are a physician meeting with a patient who has just been diagnosed with cancer. You know there are two mutually exclusive types of cancer that the patient could have: A and B. The probability that she has A cancer is 1/3. A is deadly: four patients out of five diagnosed with A cancer die within one year. Type B is less dangerous: only one patient out of five diagnosed with B cancer dies within one year. (a) What is the probability that your patient has A cancer and suc- cessfully survives it? (b) What is the probability that your patient dies within a year? (c) Suppose that your patient dies in less than one year before you learn the exact of cancer he has. Given this sad happening, what is the probability that she had A cancer? (Hint: You want to start off by considering this question: given the information provided in the story (what those numbers are really about?), which of the two analytical tools we have covered in class will be more helpful to solve this problem, a probability table or a probability tree? )