New Car. A game show gives away 2 new cars. One car is worth $50,000 and the other car is worth $40,000. Two members of the audience are randomly selected to participate and receive one of the two new cars. What is the expeted value if you are randomly chosen and you had to pay $4 to be a member of the audience with 1999 other people.
Your chances are 1/2000 of winning the $50,000 car (if it is drawn first) plus 1/1999 of drawing the second car. Expected value of the opportunity to participate is $45. If you paid $4 for that opportunity, it was a good deal.
Thanks
To calculate the expected value in this scenario, we need to consider the probabilities of winning each car and the respective values of the cars.
Here's how you can calculate the expected value:
1. Determine the probability of winning each car:
- Since there are 2001 total participants (you plus the other 1999 people), and two cars to be given away, the probability of winning each car is 1/2001.
2. Calculate the expected value for each car:
- Car 1: Probability of winning (1/2001) multiplied by the value of the car ($50,000).
- Car 2: Probability of winning (1/2001) multiplied by the value of the car ($40,000).
3. Sum up the expected values:
- Add the expected values of Car 1 and Car 2 to determine the overall expected value.
Let's do the calculations:
Expected value of Car 1 = (1/2001) * $50,000 = $24.99
Expected value of Car 2 = (1/2001) * $40,000 = $19.99
Overall expected value = Expected value of Car 1 + Expected value of Car 2
= $24.99 + $19.99
= $44.98
Therefore, if you are randomly chosen and had to pay $4 to be a member of the audience, the expected value is $44.98.