Final answer:
Without the specific probability of the basketball player making the next 22 free throws, we cannot calculate the expected value. Generally, the expected value is calculated by considering probabilities of outcomes and the respective gains or losses, which inform whether the proposition is favorable in the long run.
Step-by-step explanation:
The question concerns the calculation of the expected value in a probabilistic scenario in mathematics. To calculate the expected value of the proposition described in the question, we would follow these steps:
- First, determine the probabilities of the player making and missing the next 22 free throws. This requires previous performance data, which might be given or assumed based on the player's free-throw percentage.
- Second, calculate the expected value by multiplying the outcome values (money won or lost) by their probabilities and summing the products.
However, without specific probabilities, calculation of the exact expected value cannot be done. For the purpose of this example, let's assume the basketball player makes the next 22 free throws with a probability of 'p' and misses with a probability of '1-p'. If he makes them, you win $32, and if he misses them, you lose $21. Using the formula for expected value:
E(X) = (Winning Amount × Probability of Winning) + (Losing Amount × Probability of Losing)
The expected value would then be:
E(X) = ($32 × p) + (-$21 × (1-p))
To interpret the result, if the expected value is positive, playing the game repeatedly would net a profit on average over time; if it is negative, it would result in a loss.
Without knowing the probability 'p', we cannot complete the calculation or give a definitive answer. Normally, you would need to use the free-throw success rate to estimate 'p', but since the question contains a typo we can't do this here.