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Five children are selected at random from a class containing 10 boys and 20 girls. Find the probability that exactly 2 boys are selected.

I'm thinking: $$\frac{{10 \choose 2}*{20 \choose 3}}{{30 \choose 5}}=\frac{45*1140}{142506}=\frac{51300}{142506}=0.35998(5dp)$$

But the book gives an answer of: $\frac{80}{243}$ which is $0.32922(5dp)$.

Did I do something wrong, or is the answer in the book wrong ?

  • 2
    It looks to me like your answer is correct. – 2017-02-20
  • 1
    hypergeometric distribution, seems to be correct. – 2017-02-20
  • 1
    Your answer seems correct, there may be some error in the book. – 2017-02-20
  • 0
    Thanks all. I'm satisfied my method and result are both correct. – 2017-02-20

0 Answers 0