In its Flip Your 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 a sports car worth $35 000. A total of 1 000 000 promotional coffee cups have been printed for this contest. Coffee sells for $1.50 per cup. What is the expected value of a cup of coffee to the consumer?
Expected value = the sum of (the probability times the number of opportunites).
that is hint #1
Can you work with that?
MsPi_3.14159265:
Can you explain little bit pls
To determine the expected value of a cup of coffee to the consumer, we need to calculate the probability and value of each potential prize, and then sum them up.
First, let's calculate the probability of winning a specific prize:
- The probability of winning one of the 50 000 free coffees is 50 000 / 1 000 000 = 0.05.
- The probability of winning one of the two new TVs is 2 / 1 000 000 = 0.000002.
- The probability of winning the snowmobile is 1 / 1 000 000 = 0.000001.
- The probability of winning the sports car is also 1 / 1 000 000 = 0.000001.
Next, let's calculate the value of each prize:
- The value of a free coffee is $1.50.
- The value of each TV is $1200.
- The value of the snowmobile is $15 000.
- The value of the sports car is $35 000.
Now, let's calculate the expected value by multiplying each prize's probability by its corresponding value, and then summing them up:
Expected value = (Prize 1 probability x Prize 1 value) + (Prize 2 probability x Prize 2 value) + (Prize 3 probability x Prize 3 value) + (Prize 4 probability x Prize 4 value)
Expected value = (0.05 x $1.50) + (0.000002 x $1200) + (0.000001 x $15 000) + (0.000001 x $35 000)
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 consumer is approximately $0.1274.
To calculate the expected value of a cup of coffee to the consumer, we need to calculate the probability of winning each prize and the value of each prize.
First, let's calculate 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.
Next, let's calculate the value of each prize:
- The value of one free coffee is $1.50.
- The value of one TV is $1200.
- The value of the snowmobile is $15,000.
- The value of the sports car is $35,000.
Now, we can calculate the expected value. The expected value is the sum of the product of each prize's probability and value.
Expected value = (Probability of winning a free coffee x Value of a free coffee)
+ (Probability of winning a TV x Value of a TV)
+ (Probability of winning a snowmobile x Value of a snowmobile)
+ (Probability of winning a sports car x Value of a sports car)
Expected value = (1/20 x $1.50) + (1/500,000 x $1200) + (1/1,000,000 x $15,000) + (1/1,000,000 x $35,000)
Now let's calculate each term:
(1/20 x $1.50) = $0.075
(1/500,000 x $1200) = $0.0024
(1/1,000,000 x $15,000) = $0.015
(1/1,000,000 x $35,000) = $0.035
Finally, we can add up all the terms to get the expected value:
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 consumer is approximately $0.13.