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Each day the price of a new computer stock moves up one point or down one point with probabilities 0.75 and 0.25. What is the probability that by the end of the sixth day the stock will have returned to its original price (the price today, day 0)?

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To return to the original value, the price should go up three times and down three times. So you need exactly 3 successful trials out of 6. You can measure that probability with a Binomial distribution:

$P(3;6,0.75) = \binom{6}{3}0.75^30.25^3 \approx 0.132$

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