In a basketball game a single basket could count for 1 point (a free throw), 2 points (a basket initiated inside the 3-point line), or 3 points (a basket initiated outside the 3-point line). If Leroy makes 4 baskets in the next game, what is the sample space for the possible number of points he could score?Group of answer choices{4,5,6,7,8,9,10,11,12}{1,4,5,6,7,8,9,10,11,12}{3,4,5,6,7,8,9}{2,3,4,5,6}{1,2,3,4,5,6}
Question
In a basketball game a single basket could count for 1 point (a free throw), 2 points (a basket initiated inside the 3-point line), or 3 points (a basket initiated outside the 3-point line). If Leroy makes 4 baskets in the next game, what is the sample space for the possible number of points he could score?Group of answer choices{4,5,6,7,8,9,10,11,12}{1,4,5,6,7,8,9,10,11,12}{3,4,5,6,7,8,9}{2,3,4,5,6}{1,2,3,4,5,6}
Solution
The sample space for the possible number of points Leroy could score in the next game, given that he makes 4 baskets, would be {4,5,6,7,8,9,10,11,12}.
Here's why:
- If Leroy scores all his baskets as free throws, he would score 1 point per basket. So, 4 baskets would give him 4 points.
- If Leroy scores all his baskets as 2-pointers, he would score 2 points per basket. So, 4 baskets would give him 8 points.
- If Leroy scores all his baskets as 3-pointers, he would score 3 points per basket. So, 4 baskets would give him 12 points.
However, Leroy could also score a combination of 1-point, 2-point, and 3-point baskets. This means he could score any total number of points between the minimum (4) and the maximum (12). Therefore, the sample space is {4,5,6,7,8,9,10,11,12}.
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