E1. In the recent Canadian election 33% of people voted for Justin Trudeau. If you were to randomly select 450 people who voted, what is the probability that fewer than 160 voted for Trudeau?

E2. You read that as of Nov 15 2021, 89% of Canadians 12 or older now have at least 1 dose of a COVID vaccine. If you randomly select 8 people, what is the probability that exactly 6 has had at least one dose of a vaccine?

E3. Several professors have noted that violations of academic integrity have increased since courses went online so efforts to discourage but also monitor these activities have been increased. An organization studying this has estimated that only 55% of students who inappropriately share materials on a test, exam or assignment get caught. If a student submits information on 4 assignments in violation of the rules what is the probability they will not be noticed (i.e. they will NOT get caught). What is the probability that they will get caught at least once?

E4. A deck of cards has 52 cards. These are split evenly into 4 suits (spades and clubs that are black, and hearts and diamonds that are red) and there are 13 cards in each suit. You select one card, record what suit it is and then replace it back in deck and shuffle the deck before selecting the next card. If you select 5 cards in this manner what is the probability that fewer than 3 will be Clubs?