The sample space below shows the results of the final eight matches played by the English soccer team Manchester United during their championship 2012-20132012−20132012, minus, 2013 season. They won matches where they scored more goals than their opponent, lost matches where they scored less, and tied matches where they scored the same amount. If we take matches 1, 3, 5, 6, and 8 as a subset of the sample space, which of the statements below describe this subset?

a. The subset consists of all the matches where Manchester United's opponent did not win.
b. The subset consists of a the matches where Manchester United's opponent did not lose.
c. The subset consists of an the matches where Manchester United did not win.
d. The subset consists of all the matches where there was a tie.

Manchester United Opponent
Match 1 1 2
Match 2 2 0
Match 3 2 2
Match 4 3 0

Q.1 dr. frank needs to choose 3 students from her advanced biology course to attend a conference in hawaii. the course has 40 students. which of the following methods could dr. frank use to choose a simple, random sample of 3 students? select all that apply. 1 dr. frank could have the students line up from shortest to tallest, then use her birthdate, 2/5/39, to select 3 students from the line (the 2nd student, the 5th student, and the 39th student). 2. dr. frank could upload her class roster into a spreadsheet and use a ranom-number generating function to produce 3 random numbers. the students whose names are located in the rows with these 3 numbers on the spreadsheet would be chosen. 3. dr. frank could choose the students with the 3 highest grades in the class. 4. dr. frank could count to three, then the first students to come to the front of the classroom and grab a golden ticket from her hand would be selected. 5. dr. frank could ask all students to write their name on a card, place all of the cards in a hat, shake the hat, and then pull 3 cards out from the hat. the students whose names appear on those 3 cards will be selected. 6. dr. frank could ask for volunteers to go to the conference, then choose the first 3 students who raise their hands. q2. now, choose one of the methods that you did not select and explain why this method would not result in a simple, random sample: