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4.4 Hypergeometric Distribution

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Presentation on theme: "4.4 Hypergeometric Distribution"— Presentation transcript:

1 4.4 Hypergeometric Distribution

2 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.

3 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.

4 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.

5 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

6 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

7 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

8 Binomial and Hypergeometric
They are VERY similar Binomial has Independent events Hypergeometric has Dependent Events

9 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.

10 Hypergeometric Distribution

11 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

12 Assignment Page 178 #’s 1-7,10, 11


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