Answer: a) -$0.19, b) -$111.72 .
Step-by-step explanation:
Since we have given that
Number of free throws = 434
Number of throws made by them = 390
Amount for making the next 2 free throws = $40
Amount otherwise he has to pay = $169
a) Find the expected value of the proposition.
Expected value of success in next 2 free throws = ![\dfrac{390}{434}\times \dfrac{391}{435}=0.8077](https://tex.z-dn.net/?f=%5Cdfrac%7B390%7D%7B434%7D%5Ctimes%20%5Cdfrac%7B391%7D%7B435%7D%3D0.8077)
Expected value would be
![0.8077\times 40+(1-0.8077)\times -169\\\\=32.308-32.4987\\\\=-\$0.19](https://tex.z-dn.net/?f=0.8077%5Ctimes%2040%2B%281-0.8077%29%5Ctimes%20-169%5C%5C%5C%5C%3D32.308-32.4987%5C%5C%5C%5C%3D-%5C%240.19)
b) If you played this game 588 times how much would you expect to win or lose?
Number of times they played the game = 588
So, Expected value would be
![588\times -0.19\\\\=-\$111.72](https://tex.z-dn.net/?f=588%5Ctimes%20-0.19%5C%5C%5C%5C%3D-%5C%24111.72)
Hence, a) -$0.19, b) -$111.72