two gamblers are playing a coin toss game. gambler a has (n 1) fair coins; b has n fair coins. what is the probability that a wi

two gamblers are playing a coin toss game. gambler a has (n 1) fair coins; b has n fair coins. what is the probability that a will have more heads than b if both flip all their coins

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1. thienthanh
Gambler A loses his comparative advantage the more coins that are tossed for both Gamblers. But Gambler A will always maintain the advantage and has quite a heavy advantage when a few coins are tossed.
What is the binomial distribution?
The discrete probability distribution of the number of successes in a series of n independent experiments is called the binomial distribution with parameters n and p in probability theory and statistics.
Let X be the count of successes in the first n flips by A, Y the indicator that the last flip by A is also a success, and Z the count of successes in n flips by B.
Because Y is independent of X and Z, then:
P(X + Y > Z) = P(Y = 1) P(X ≥ Z) + P(Y = 0) P(X > Z)
= 1/2(P(X = Z) + 2P(X > Z))
P(X > Z) = P(Z > X)
Gambler A loses his comparative advantage the more coins that are tossed for both Gamblers. But Gambler A will always maintain the advantage and has quite a heavy advantage when a few coins are tossed.