In the following scenarios, please describe the the sample space and also indicate the total number of outcomes (if nite). It is not necessary to use rigorous mathematic notations to describe the sample space, but your answer should be precise and cover all the possible outcomes. 1) You are asked to write down the month of your birthday as shown on your passport. 2) In a class of 40 students, the teacher randomly choose one student, and ask the student to write down the month of his/ her birthday as shown on his/her passport. 3) Monty Hall problem: In a game show, a player will be given three closed envelopes, A, B and C. There is a 10,000 check in envelope A, but only empty papers in envelopes B and C. The player does not know which envelope contains the check but the game host knows. Suppose the player will choose one envelope randomly from the three envelopes without opening it. The game host then choose one envelope from the rest two and open it. The game host would make a random choice but will never open envelope A, which contains the check. The game host would then ask the player if he/she would like to change the original choice. The player can randomly choose to keep the envelope he/ she selects at the beginning and open it, or he/ she can switch to the other unopened envelope and open it. For 3), if you are interested in the event \"the player chooses to switch the envelope and get the 10,000 check as a result\