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Answer :
The probability of winning an arcade game no more than 12 times out of 24 attempts is calculated using the cumulative binomial probability formula.
However, the calculations can be complex and typically require a statistical calculator. Without these tools or further information, it's not feasible to provide a accurate numerical answer.
The subject area this question falls into is Mathematics, specifically the domain of probability. The question is asking for the probability of winning no more than 12 times out of 24 attempts in an arcade game. This problem is solved by calculating the cumulative probabilities of winning from 0 to 12 times out of 24.
However, these calculations can be very complex and are usually done with a statistical software or a calculator with a built-in cumulative binomial probability function. Unfortunately, without these tools or further information, providing an exact numerical answer to this specific question may not be possible.
Generally, the cumulative binomial probability formula is P(X ≤ k) = Σ [C(n, x) * (p^x) * ((1-p)^(n-x))] as x ranges from 0 to k. In this formula, n represents the number of trials (in this case, 24 plays of the arcade game), p represents the probability of success on each trial (the chance of winning here, which is 0.626), x represents the number of successful trials, and C(n, x) is a function that calculates the number of combinations of n items taken x at a time.
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