Combined hypergeometric and binomial

A question is this type if and only if it involves both sampling without replacement (hypergeometric) and sampling with replacement (binomial) in different parts of the same question.

2 questions · Standard +0.3

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Edexcel AS Paper 2 2023 June Q5
8 marks Standard +0.3
  1. Julia selects 3 letters at random, one at a time without replacement, from the word
\section*{VARIANCE} The discrete random variable \(X\) represents the number of times she selects a letter A.
  1. Find the complete probability distribution of \(X\). Yuki selects 10 letters at random, one at a time with replacement, from the word \section*{DEVIATION}
  2. Find the probability that he selects the letter E at least 4 times.
OCR S2 2012 January Q5
10 marks Standard +0.3
  1. Six prizes are allocated, using random numbers, to a group of 12 girls and 8 boys. Calculate the probability that exactly 4 of the prizes are allocated to girls if
    1. the same child may win more than one prize, [2]
    2. no child may win more than one prize. [2]
  2. Sixty prizes are allocated, using random numbers, to a group of 1200 girls and 800 boys. Use a suitable approximation to calculate the probability that at least 30 of the prizes are allocated to girls. Does it affect your calculation whether or not the same child may win more than one prize? Justify your answer. [6]