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Card probability uses the Hypergeometric Distribution to calculate the probability of drawing specific cards from a standard 52-card deck without replacement. Unlike dice (with replacement), each card drawn changes the composition of the deck, making the probabilities hypergeometric rather than binomial.
Công thức
- N
- n! / (k! × (n−k)!) — combinations formula — n! / (k! × (n−k)!) — combinations formula
- K
- sum of P(X=k) + P(X=k+1) + — sum of P(X=k) + P(X=k+1) +
- n
- n! / (k! × (n−k)!) — combinations formula — n! / (k! × (n−k)!) — combinations formula
- k
- sum of P(X=k) + P(X=k+1) + — sum of P(X=k) + P(X=k+1) +
Hướng dẫn từng bước
- 1Hypergeometric: P(X=k) = C(K,k) × C(N−K, n−k) / C(N,n)
- 2N = deck size (52), K = cards of target type, n = hand size, k = desired count
- 3C(n,k) = n! / (k! × (n−k)!) — combinations formula
- 4P(at least k) = sum of P(X=k) + P(X=k+1) + ... + P(X=K)
Ví dụ có lời giải
Câu hỏi thường gặp
What is Card Probability?
Card probability uses the Hypergeometric Distribution to calculate the probability of drawing specific cards from a standard 52-card deck without replacement. Unlike dice (with replacement), each card drawn changes the composition of the deck, making the probabilities hypergeometric rather than binomial
How accurate is the Card Probability calculator?
The calculator uses the standard published formula for card probability. Results are accurate to the precision of the inputs you provide. For financial, medical, or legal decisions, always verify with a qualified professional.
What units does the Card Probability calculator use?
This calculator works with inches. You can enter values in the units shown — the calculator handles all conversions internally.
What formula does the Card Probability calculator use?
The core formula is: Hypergeometric: P(X=k) = C(K,k) × C(N−K, n−k) / C(N,n). Each step in the calculation is shown so you can verify the result manually.
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