Suppose a basketball player has made 234 out of 305 free throws. if the player makes the next 3 free throws, i will pay you $10. otherwise you pay me $7. find the expected value of the proposition.

The player shooting 390/434 is a free throw percentage of 89.86%.  We can now estimate his probability of making the next 2 shots as (.8986)^2 = .8075.

So now to find the expected value, you just need to find the value of each possible outcomes (he makes both or he doesn't).

P(makes both) * (Value when you win) + P(misses both) * (value when you lose)

.8075 * $40 + (1-.8075)*(-$169)

32.2 - 32.53

= -$.23

For the second part, you already know the expected value of each possible game. So now you just need to multiply that by 588 to get your expected loss on 588 games.

chad should not have included the values (1, 2) and (3, 6) because that would mean he only had half a healing card.