Expected Value of Cup of Coffee in Flip a Lid Contest

• MHB
• Istar
In summary, a coffee chain is running a flip a lid contest where they are offering prizes of 50,000 free coffees, two new TVs, a snowmobile, and a sports car. A total of 1,000,000 promotional coffee cups have been printed for the contest. Each cup of coffee sells for $1.50. The expected value of a cup of coffee to the customer is approximately -$1.37, taking into account the certainty of spending $1.50 to purchase the cup. Istar In its flip a lid contest, a coffee chain offers prizes of 50,000 free coffees, each worth \$1.50; two new TVs, each worth \$1200; a snowmobile worth \$15 000; and sports car worth \$35 000. A total of 1 000 000 promotional coffee cups have been printed for contest. Coffee sells for \$1.50 per cup. What is the expected value of cup of coffee to the customer?

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Hello, and welcome to MHB! :)

To begin, we need to determine the probabilities for the following events:
• Customer who bought a cup of coffee, purchased a cup of coffee (this is certain, thus probability is 1)
• Customer won a free coffee
• Customer won TV
• Customer won snowmobile
• Customer won sports car
Once we've determined these probabilities, we can associate the net loss/gain for each event and compute the sum of the products of the probabilities and loss/gain for all events to determine the expected value. What do you get for the probabilities of the events?

This is how I did it :

 X P(X=x)​ 50000/1000000 1.5​ 2/1000000 1200​ 1/1000000 15000​ 1/1000000 35000​
Expected mean value [x] = {x(Px)} =

(0.05x1.5) + (0.000002x1200) + (0.000001x15000) + (0.000001x35000) =

(.075) + (0.0024) + (0.015) + (0.035) = 0.1274

I am not sure if it right !

I would write:

$$\displaystyle E[X]=1(-1.5)+\frac{50000}{1000000}(1.5)+\frac{2}{1000000}(1200)+\frac{1}{1000000}(15000)+\frac{1}{1000000}(35000)=-\frac{6863}{5000}\approx-1.37$$

What factors can affect the expected value in a flip a lid contest?

The expected value can be affected by the probability of winning, the value of the prize, and the cost of participating in the contest. It can also be influenced by any additional rules or restrictions of the contest.

Is the expected value a guarantee of what I will receive in a flip a lid contest?

No, the expected value is not a guarantee of what you will receive in a flip a lid contest. It is simply an average value that you can expect to receive over multiple attempts. You may receive more or less than the expected value in any given attempt.

Why is it important to consider the expected value in a flip a lid contest?

Considering the expected value is important because it helps you make an informed decision about whether or not to participate in the contest. If the expected value is low, it may not be worth the cost of participating. It can also help you compare the value of different contests and choose the one with the highest expected value.