1. Assuming each day you drive to work a traffic light that you encounter is either green with probability 3/8, red with probability ½, or yellow with probability 1/8, independent of the status of the light on any other day. If over the course of 4 days, G, Y, and R denote the number of times the light is found to be green, yellow, or red, respectively. a) What is the probability that P[G=1, Y=2, R=1]? b) What is the probability P[G=Y]? 2. Consider a binary code with 7 bits (0 o 1) in each code word. An example of a code word is 0101011. In each code word, a bit is a zero with probability 0.7, independent of any other bit. a) What is the probability of the code word 0011011 ? b) What is the probability that a code word contains exactly two ones? 3. An urn contains 4 black and 6 white balls. Person A and person B withdraw balls from the urn consecutively and without replacement of the balls drawn until a black ball is selected. Find the probability that person A is the one who selects the black ball. (Note: person A draws the first ball, then person B, then again A, and so on.) 4. Six people, designated as A, B, C, D, E, and F, are arranged in linear order. Assuming each possible order is equally likely, find the probability of the following events: a) there is exactly one person between A and B, b) there are exactly two people between A and B, c) there are four people between A and B. 5. A fair coin is tossed three times and the random variable X equals the total number of heads. Find and sketch the cumulative distribution and probability mass function of X. I have 5 midterm questions example what do you think about this question?