A Galton board drops balls through 12 rows of pegs, and at each peg a ball goes left or right with probability ½. Bin k collects the balls that went right exactly k times, and C(12, k) of the 2¹² equally likely paths do that, so P(k) = C(12, k)/2¹². The middle bin gets 924/4096

Name: A Galton board drops balls through 12 rows of pegs, and at each peg a ball goes left or right with probability ½. Bin k collects the balls that went right exactly k times, and C(12, k) of the 2¹² equally likely paths do that, so P(k) = C(12, k)/2¹². The middle bin gets 924/4096
Channel: matharium
Description: A Galton board drops balls through 12 rows of pegs, and at each peg a ball goes left or right with probability ½. Bin k collects the balls that went right exactly k times, and C(12, k) of the 2¹² equally likely paths do that, so P(k) = C(12, k)/2¹². The middle bin gets 924/4096

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A Galton board drops balls through 12 rows of pegs, and at each peg a ball goes left or right with probability ½. Bin k collects the balls that went right exactly k times, and C(12, k) of the 2¹² equally likely paths do that, so P(k) = C(12, k)/2¹². The middle bin gets 924/4096

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