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4.4 Hypergeometric Distribution
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Picking Prizes 6 doctors and 19 nurses attend a small conference. All 25 names are put in a hat and 5 names are randomly picked without replacement. Create the probability distribution for the number of doctors picked.
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Picking tiles Create a the probability distribution for the number of red tiles selected when picking 4 tiles. One tiles is selected at a time from four red and three green but that tile is NOT replaced back into the tile.
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Committee A committee of 6 people is to be formed from a pool of six grade 11 students and seven grade 12 students. Find the probability distribution for the number of grade 11 students selected.
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Committee Distribution
Number of Grade 11's Picked Probability 0.004 1 0.073 2 0.31 3 0.41 4 0.18 5 0.02 6
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Hypergeometric Distribution
Characteristics Random variable is number of times something happens The scenario entails a success of fail decision. (prime vs not prime, head vs not head, pass vs fail) There are n trials Dependent Events
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Hypergeometric Distribution
𝑃 𝑥 = 𝐶 𝑎,𝑥 ∗𝐶(𝑛−𝑎,𝑟−𝑥) 𝐶(𝑛,𝑟) 𝐸 𝑋 = 𝑟𝑎 𝑛 a is number of successful outcomes available in a population of size n
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Binomial and Hypergeometric
They are VERY similar Binomial has Independent events Hypergeometric has Dependent Events
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Cards A five-card hand is dealt from a standard deck of cards.
Show the probability distribution for the number of hearts in the hand.
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Hypergeometric Distribution
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Expected Value for the number of Hearts
Number of Hearts Picked Probability x*P(x) 0.22 1 0.41 0.411 2 0.27 0.549 3 0.08 0.245 4 0.01 0.043 5 0.0005 0.003 Expected Value 1.25
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Assignment Page 178 #’s 1-7,10, 11
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