If A has m=12 coins and B has n=13 coins. Coins are fair and the same. Both players throw their coins and observe the number of heads. What is the probability that B obtains more heads than A?
answer:
Obviously the probability is 0.5. I solve it with simulation of tossing coins for two persons. The simulation has parameters m and n and number of simulate step k. I use binomial random numbers and answer is the confidence interval of the above probability, winning B.
# R code for answer of The probability
m=12; n=13; k=1000
a=rep(0, times=k)
for(i in 1:k)
a[i] = sum(rbinom(k, n, 0.5) > rbinom(k, m, 0.5))
print('95% Confidence Interval for the winning probability: ')
print(paste(mean(a) / k ,' +- ', sd(a/k) / sqrt(k) * 1.96))
# answer: 0.5 +- 0.01
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