Use the following information for all steps in this problem. Input all answers to three decimals places and do not input your answers as a percentage.

Alec is taking both a Statistics course and a Geography course this semester. The probability that he passes his Statistics course is 0.65. The probability that he passes his Geography course is 0.92. These two events (passing Statistics and passing Geography) are independent.

1. What is the probability he passes both classes?

2. What is the probability he passes one class, but fails the other?

3. What is the probability he passes at least one class?

4. What is the probability he passes neither class?

5. What is the probability he passes Statistics and fails Geography?

6. What is the probability he passes Geography and fails Statistics?

How are your grades? In a recent semester at a local university, 3oo students a: enrolled in both Statistics I and Psychology 1. Of these students, as got an A 4') in statistics, is: got an a in psychology, and 44 got an A in both statistics and E: psychology. Round the answers to four decimal places, as needed. Q E1 d]: (a) Find the probability that a randomly chosen student got an A in E statistics or psychology or both. The probability that a randomly chosen student got an A in statistics or psychology or both is D. ms at: (b) Find the probability that a randomly chosen student did not get an A in statistics. The probability that a randomly chosen student did not get an A In statistics is D. 6. Suppose that the probability of being tutored in Statistics is 0.55, while the probability of being tutored in Physics is 0.32, and the probability of being tutored in both Statistics and Physics is 0.09. a) What is the probability of being tutored in Statistics or Physics? b) What is the probability of not being tutored in Statistics nor Physics? c) Are the events "being tutored in Statistics" and "being tutored in Physics" mutually exclusive? Explain.At Floyd's Bait Shop and Upstairs University, 90% of freshmen take Statistics. 80% of those who don't take Statistics take Interpretive Dance, while only 50% of those who do take Statistics take Interpretive Dance. 1) What is the probability that a freshman takes Interpretive Dance? 2) What is the probability that a freshman who takes Interpretive Dance doesn't take Statistics? 3) Illustrate this probability model with a tree or Venn diagram