高校数学の質問スレ Part441

[過去ﾛｸﾞ] 高校数学の質問スレ Part441 (1002ﾚｽ)
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215: １３２人目の素数さん [sage] 2025/04/28(月) 14:01:36.81 ID:FqERNgkc

>>213
Rだと分数表示させるのが面倒。経験上、gmpは今ひとつ信頼性にかける。

library(gmp)

# Hypergeometric PMF (returns a fraction)
pmf = function(m, N, n, r) {
num = mul.bigz(chooseZ(m, r), chooseZ(N - m, n - r))
den = chooseZ(N, n)
as.bigq(num, den)
}

N_total = 600    # Total number of students
n_sample = 30    # Number of sampled students
r_observed = 13  # Number of girls observed in the sample

# Precompute the denominator once
denominator = chooseZ(N_total, n_sample)

# Vector of all possible m (0 to 600)
m_vec = 0:N_total

# Use sapply
pmf_vec = sapply(m_vec, function(m) {
num = mul.bigz(chooseZ(m, r_observed), chooseZ(N_total - m, n_sample - r_observed))
as.bigq(num, denominator)
})

# Total probability (normalization constant)
total = Reduce('+', pmf_vec)

# Sum over m >= 300
numerator = Reduce('+', pmf_vec[301:601])  # 301:601 because R is 1-based indexing

# Conditional probability
prob = numerator / total

# Display result
print(prob)            # Fraction output
print(asNumeric(prob)) # Numeric (decimal) output if needed

http://rio2016.5ch.net/test/read.cgi/math/1745555217/215

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