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?
total prizes: 50000+2+1+1 = 50004
so multiply each prize by its chances of being drawn, and add them up:
50000/1000000 * 1.50
+ 2/1000000 * 1200
+ ...
To calculate the expected value of a cup of coffee for the customer, we need to determine the probability of winning each prize and multiply it by the value of that prize. Then, we sum up all the values to obtain the expected value.
Given information:
- Prizes:
- 50,000 free coffees worth $1.50 each
- 2 new TVs worth $1,200 each
- 1 snowmobile worth $15,000
- 1 sports car worth $35,000
- Total number of promotional coffee cups printed for the contest: 1,000,000
Now let's calculate the expected value step-by-step:
1. Calculate the probability of winning each prize:
- Probability of winning a free coffee: 50,000 / 1,000,000 = 0.05
- Probability of winning a TV: 2 / 1,000,000 = 0.000002
- Probability of winning a snowmobile: 1 / 1,000,000 = 0.000001
- Probability of winning a sports car: 1 / 1,000,000 = 0.000001
2. Calculate the value of each prize:
- Value of a free coffee: $1.50
- Value of a TV: $1,200
- Value of a snowmobile: $15,000
- Value of a sports car: $35,000
3. Calculate the expected value:
Expected value = (Probability of winning a free coffee * Value of a free coffee)
+ (Probability of winning a TV * Value of a TV)
+ (Probability of winning a snowmobile * Value of a snowmobile)
+ (Probability of winning a sports car * Value of a sports car)
Expected value = (0.05 * $1.50) + (0.000002 * $1,200) + (0.000001 * $15,000) + (0.000001 * $35,000)
Calculating the above expression will give us the final expected value.
To find the expected value of a cup of coffee to the customer, we need to calculate the probability of winning each prize and multiply it by the value of that prize. Then, we sum up the products to get the expected value.
First, let's determine the probability of winning each prize:
- The probability of winning one of the 50,000 free coffees is 50,000/1,000,000 = 1/20.
- The probability of winning one of the two new TVs is 2/1,000,000 = 1/500,000.
- The probability of winning the snowmobile is 1/1,000,000.
- The probability of winning the sports car is 1/1,000,000.
Now, let's calculate the expected value:
Expected Value = (Probability of winning a free coffee * Value of a free coffee)
+ (Probability of winning a TV * Value of a TV)
+ (Probability of winning a snowmobile * Value of a snowmobile)
+ (Probability of winning a sports car * Value of a sports car)
Expected Value = (1/20 * $1.50) + (1/500,000 * $1200) + (1/1,000,000 * $15,000) + (1/1,000,000 * $35,000)
Calculating this expression:
Expected Value = $0.075 + $0.0024 + $0.015 + $0.035
Expected Value = $0.1274
Therefore, the expected value of a cup of coffee to the customer is approximately $0.1274.
50000/1000000 1.5
2/1000000 1200
1/1000000 15000
1/1000000 35000
(0.05x1.5) + (0.000002x1200) + (0.000001x15000) + (0.000001x35000) =
(.075) + (0.0024) + (0.015) + (0.035) = 0.1274
I am right ?