you throw 1000 darts. each one has a 50% chance to score. for the first 500 darts each is worth 1 point, for the second 500 darts each is worth 3 points. if you score 1500 points. most likely how many 3 point darts have you scored.

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15-11-2022
Mathematics

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you throw 1000 darts. each one has a 50% chance to score. for the first 500 darts each is worth 1 point, for the second 500 darts each is worth 3 points. if you score 1500 points. most likely how many 3 point darts have you scored.

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contexto1212 contexto1212 · Answer 1 · 2022-11-20T11:03:22-05:00

Most likely I have scored 375 3-point darts.

The expected (mean) value of the total points is as follows, with a 50% chance of scoring 1-point darts and the same for 3-point darts:50 percent of the 500-point darts score and 50 percent of the 500-point darts score. The anticipated number of points is 1 point multiplied by 1/2 (500) times 3 points yielding 1000 points.

The equality of distribution between the 1-point and 3-point scoring indicates that you scored 1500/1000, or 1.5 times the means, assuming that you actually scored 1500 points in total. That indicates that 1500 points are equal to 1.5 (.5) 500 (1 point) plus 1.5 (.5) 500 (3 points). Therefore, you scored 1.5 (.5) 375 3-point dart hits.

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