3. Consider a class of 30 students. Surprisingly, the probability that at least two of them will have same birthday turns out to be more than 70%. To demonstrate this by simulation, let's randomly generate each person's birthday. Count the number of matches among the 30 students; if more than two students have the same birthday count it as one match. a. Simulate the above situation 1000 times and determine the probability distribution of the number of matches. In particular, compute the chances that at least two persons have the same birthday. [Hint: Use =RANDBETWEEN{1,365) to generate a random birthday; i.e., an integer between 1 to 365. In addition, use =COUNTIF function to \"count\" a match that meets certain criteria] b. What is the average number of birthday matches? What is the standard deviation? c. Draw the probability distribution of birthday matches for the 30 student classroom