2. Mike and John are playing a friendly game of darts where the dart board is a

Question

2. Mike and John are playing a friendly game of darts where the dart board is a disk of a radius of 10 inches. Whenever a dart falls within 1 inch of the center (the bullseye), then 50 points are scored. If the point of impact is between 1 and 3 inches from the center, then 30 points are scored, if it is at a distance of 3 to 5 inches, then 20 points are scored and if it is further than 5 inches, then 10 points are scored. Assume that both players are skilled enough to be able to throw the dart within the boundaries of the board. Mike can place the dart uniformly on the board (i.e. the probability of the dart falling in a given region is proportional to its area.) (a) What is the probability that Mike scores 50 points on one throw? (b) What is the probability of him scoring 30 points? (c) John is right handed and is twice more likely to throw in the right half of the board than in the left half. Across each half, the dart falls uniformly in that region. Answer the previous questions for John's throw.

Explanation / Answer

a) probability mark score 50 points = (inches he need to aim into)/(total inches) => 1/10

B) probability of 30 points = (3-1)/10 => 2/10 => 1/5

C) the probability will remain same as the chances of excessively hitting in the left portion will be overcome by the reductions chances of hitting in the right as the dart is perfectly round shaped

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