6. [20 pts] You decide to stand at a busy intersection and count the number of cars going through that intersection for sixty minutes. (a) [4 pts] Define the following sample spaces. Define notations as necessary. (i) Number of cars passing through the intersection. (ii) Time (in minutes) until you observe the first car to pass through that intersection. (b) [6pts] What type of variable are the following? (i) Color of the first car you observe. (ii) Number of cars passing through the intersection. (iii) Time (in minutes) until you observe the first car to pass through that intersection. (c) [10pts] Consider the sample space for time in minutes (denoted as it) until you observe the first car to pass through that intersection. Answer the following questions (i) [4 pts] Consider the following events/sets. {t: 10 30} denoted as B. Are the events mutually exclusive? Are the events independent? Provide intuitive explanations. (ii) [6 pts] Consider the following events/sets. {t: 10 S t