Question

1. A club is hosting a raffle to raise money. I buy one of 200 raffle tickets for $10. There is one prize, which is a free 3-credit NSCC course valued at $618. Create a probability distribution for this raffle and calculate my expected value of buying a single ticket.

2. Another club is hosting a raffle to raise money which offers cash prizes. I buy one of 5,000 raffle tickets for $1. The club officials will randomly select one grand prize worth $1000, two-second prizes worth $500 each, and three third prizes at $250 each. Create a probability distribution for this raffle and calculate my expected value of buying a single ticket.

3. An insurance company insures a person’s antique coin collection worth $30,000 for an annual premium of $200. The company figures that the probability of the collection being stolen is 0.0014.
   1. What will be the company’s expected profit on this policy?

2. What will be the company’s break-even price? (i.e. the price a company should charge if they wanted to make zero profit or loss)

4. You are taking a 15-question multiple choice quiz and each question has 5 options (a,b,c,d,e) and you randomly guess every question.
   1. How many questions do you expect to answer correctly on average?

2. What is the probability that you get every question correct?

3. What is the probability that you get every question incorrect?

5. Consider still the 15-question multiple choice quiz that each question has 5 options (a,b,c,d,e) and you randomly guess every question.
   1. How many questions does one need to answer correctly in order score exactly 60%?

2. If a grade of 60% or lower is considered failing, then what is the probability of you failing?

3. If you need a grade of 80% or higher on this quiz to maintain a passing grade, what is the probability of you maintaining that passing grade?

Answer 1