Dart Probability

Probability Level 2

Albert is playing a game of darts. If he hits a target, he gains one point, if he misses, he doesn’t get a point. Assuming Albert has a 5 6 \displaystyle{5\over{6}} chance of hitting the target and he has 4 4 darts, what is the probability that Albert gets 0 0 points?

Another interesting problem

1 5 \displaystyle 1\over{5} 1 256 \displaystyle 1\over{256} 1 36 \displaystyle 1\over{36} 1 1296 \displaystyle 1\over{1296} 1 2 \displaystyle 1\over{2}

Just C by Just C , 15, Hong Kong

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1 solution

Just C
May 15, 2021

The probability of Albert getting 0 0 points can be rephrased as the probability that Albert misses all 4 4 darts. Since Albert has a 5 6 \displaystyle{5\over{6}} chance of hitting the target, he must have a 1 6 \displaystyle{1\over{6}} chance of missing the target. So missing four times in a row has a probability of:

1 6 × 1 6 × 1 6 × 1 6 = 1 6 4 = 1 1296 \displaystyle{{1\over{6}}\times{1\over{6}}\times {1\over{6}}\times {1\over{6}}={1\over{6^4}}={\boxed{1\over{1296}}}}

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