Question

consider the probability of landing in the 40-point hole to complete these sentences. if the size of the 40-point hole is enlarged, the probability drop-down. if the 40-point hole is made smaller, the probability drop-down. if the 40-point hole stays the same size, but the scoring zone is made smaller, the probability drop-down.

Explanation:

To solve this, we analyze the relationship between the size of the 40 - point hole and the probability of landing in it, based on the concept of probability related to the area (or size) of a target:

Sentence 1: If the size of the 40 - point hole is enlarged, the probability...

The probability of landing in a region (the 40 - point hole) is related to the relative size of that region compared to the total area of the target (the entire board, for example). If the size (area) of the 40 - point hole is enlarged, the chance of landing in it increases. So the probability increases.

Sentence 2: If the 40 - point hole is made smaller, the probability...

When the size (area) of the 40 - point hole is reduced, the chance of landing in it becomes lower. So the probability decreases.

Sentence 3: If the 40 - point hole stays the same size, but the scoring zone is made smaller, the probability...

The scoring zone is the total area where the ball can land (or the relevant area for scoring). If the 40 - point hole size remains the same, but the scoring zone (total area) is made smaller, the relative size of the 40 - point hole compared to the scoring zone increases. For example, if the 40 - point hole area is \(A\) and the scoring zone area was \(T\) and now becomes \(T'\) where \(T'increases.

For the first blank (when 40 - point hole is enlarged): increases

For the second blank (when 40 - point hole is made smaller): decreases

For the third blank (when scoring zone is made smaller with 40 - point hole size same): increases

Answer:

To solve this, we analyze the relationship between the size of the 40 - point hole and the probability of landing in it, based on the concept of probability related to the area (or size) of a target:

Sentence 1: If the size of the 40 - point hole is enlarged, the probability...

The probability of landing in a region (the 40 - point hole) is related to the relative size of that region compared to the total area of the target (the entire board, for example). If the size (area) of the 40 - point hole is enlarged, the chance of landing in it increases. So the probability increases.

Sentence 2: If the 40 - point hole is made smaller, the probability...

When the size (area) of the 40 - point hole is reduced, the chance of landing in it becomes lower. So the probability decreases.

Sentence 3: If the 40 - point hole stays the same size, but the scoring zone is made smaller, the probability...

The scoring zone is the total area where the ball can land (or the relevant area for scoring). If the 40 - point hole size remains the same, but the scoring zone (total area) is made smaller, the relative size of the 40 - point hole compared to the scoring zone increases. For example, if the 40 - point hole area is \(A\) and the scoring zone area was \(T\) and now becomes \(T'\) where \(T'increases.

For the first blank (when 40 - point hole is enlarged): increases

For the second blank (when 40 - point hole is made smaller): decreases

For the third blank (when scoring zone is made smaller with 40 - point hole size same): increases