Question

A game involves sliding a puck onto a surface. A player is awarded points depending on where the puck halts. The height of the 3 point rectangle is 1 foot, the height of the 2 point rectangle is 2 feet, and the height of the 1 point rectangle is 3 feet. Assume that the puck always lands on one of the rectangles, and it has an equal probability of landing on any point within the scoring rectangle. What is the probability the player will be awarded 1 point?

1/6
1/3
1/2
2/3

Answer 1

Given:
3 point rectangle is 1 foot
2 point rectangle is 2 feet
1 point rectangle is 3 feet

6 feet in all.

3 points is 1/6
2 points is 2/6 or 1/3
1 point is 3/6 or 1/2

The probability that the player will be awarded 1 point is 1/2.

Answer 2

looking at the rectangle which contains all of the scoring points, the total height would be 6 feet. This is because the 3-point rectangle is 1 foot high, the 2-point rectangle is 2 feet high, and the 1-point rectangle is 3 feet high. Since we are only looking for the probability that the player is able to score 1 point, we divide the height of the 1-point rectangle by the total height. Which is:

3/6 = 1/2

Therefore, the probability is 1/2.