Question

You toss a bean bag at a board that is covered with 10 Squares. The values in the squares are the odd numbers from 1 to 9 and their opposites. Describe three ways the bean bag might land so that the value of the toss is a positive number, a negative number, and 0.

Answer 1

Three scenarios for the bean bag toss include landing on an odd numbered square for a positive value, landing on the opposite of an odd number for a negative value, and a hypothetical case where landing between two squares (positive and negative of the same number) could result in a value of zero.

Step-by-step explanation:

To describe three ways the bean bag might land so that the value of the toss is a positive number, a negative number, and zero, we can consider the following scenarios:

Positive number: The bean bag lands on any of the squares with odd numbers from 1 to 9. For example, landing on the square with the number 5 would result in a positive value of +5.

Negative number: The bean bag lands on any of the squares with the opposites (negatives) of those odd numbers. If the bag lands on the square opposite to the number 7, it will be landing on -7, resulting in a negative value.

Zero: In this context, since there is no opposite of zero (as zero is neither negative nor positive), the description of the game does not directly provide a way for the toss to value zero. However, if an additional rule is presumed where landing between two squares results in the sum of the numbers, then landing between a positive and its opposite would equal zero (e.g., landing between +3 and -3).

Remember, when considering possible game outcomes such as landing on positive, negative, or zero values, it is grounded in probability, and each toss is an independent event.

Answer 2

As for this question, there are a lot of factors to take in. Some of it would be how the board is positioned, is it on the ground or perpendicular to the ground, how hight is it from the ground, how big is it which would determine how big the square are, how are the odd number from 1 to 9 and their opposites arranged in the board, how far are you from the bean bag, and so on. Thus, when all of these are taken into consideration, the most appropriate answer to this problem would it depends on the thrower's use of force. An overexertion and the lack of force to throwing the bean bag would probably result to a 0, meaning there is none of the 10 squares that the bean bag landed. Other than that, having a target in mind while throwing and the average amount of force with the distance from the board taken into account, the chances of landing a positive number and a negative number are the same.