Final answer:
The mathematics question asks about the expected value from a game of basketball free throws. The calculated expected value is -$0.62 per game, suggesting an average loss, thus advising against playing the game to win money over repeated trials.
Step-by-step explanation:
The subject of this question is mathematics, specifically focusing on probability and expected value. The question involves calculating the expected outcome from a series of basketball free throws over multiple trials. To determine the expected value, we consider the probability of the player making three consecutive free throws and the associated payouts for winning and losing.
Firstly, the player's current free throw success rate is 230 out of 316, which would be used to estimate the likelihood of succeeding in the next three throws. The payouts are $36 for winning and $22 for losing.
The expected value calculation would involve the success probability and the payouts for the outcome. If played 706 times, based on the given rates and payouts, we find that the expected value is -$0.62 per game, indicating an average loss of 62 cents per game.
Based on the expected value, it would not be advisable to play this game for monetary gain as it results in a loss over time. This aligns with the general principle that if expected value is negative, one should expect to lose money in the long run.