Question

On the dartboard there are 20 equal sized slices labeled 1-20. The area of the whole board is 90794mm², the area double score (outer ring) is 8344mm²,the area of the triple score (inner ring) is 5177mm² and the area of single score is 76476mm². What is the probability of a randomly thrown dart scoring 1 or 12?

Answer 1

The only way to score 1 is to hit 1 in the single score zone. 12 can be scored in three possible ways: hitting 12 in the single score zone, hitting 6 in the double score zone or hitting 4 in the triple score zone.

Note that area allocated to a certain point in a zone, is (1/20)th of the area of that zone, and probability of hitting a zone is the ratio of area of that zone to the total area of the dart board.

Thus,

P(hitting 1 in the single score zone) = 76476/(20x90794)

P(hitting 12 in single score zone) = 76476/(20x90794)

P(hitting 6 in double score zone) = 8344/(20x90794)

P(hitting 4 in triple score zone) = 5177/(20x90794)

Thus probability of scoring 1 or 12 is the sum of the above quantities:

(76476+76476+ 8344+5177)/(20x90794)

= 166473/1815880

= 0.0917 (Ans.)