Nusfosdsap lecture 12 8 gem2900 understanding

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Unformatted text preview: 364 × ... × 343 = 1− ≈ 0.507 365 × 365 × ... × 365 365 23 n 23 We have made C 2 1 = C 2 = 253 paired comparisons. NUS/FOS/DSAP Lecture 12 – 8 GEM2900 - Understanding Uncertainty & Statistical Thinking Semester 2, 2010/2011 How to Calculate with Probabilities √ In inverse birthday problem, we have greater than 50% chance of finding at least one match when comparing a specific birthday with birthdays of the other n2 = 253 people. P(at least someone shared my birthday among 253 people) ⎛ 364 ⎞ = 1− ⎜ ⎟ ⎝ 365 ⎠ 253 ≈ 0.501 In this case, we have made 253 paired comparisons. NUS/FOS/DSAP Lecture 12 – 9 GEM2900 - Understanding Uncertainty & Statistical Thinking Semester 2, 2010/2011 How to Calculate with Probabilities √ Notice that we have made the same number of comparisons in birthday and inverse birthday problems n 23 ( C 2 1 = C 2 = 253 = n2 ), and 365 × 364 × ... × 343 ⎛ 364 ⎞ 1− ≈ 1− ⎜ ⎟ 365 23 365 ⎠ ⎝ 253 365 × 364 × ... × ( 365 − n1 + 1) ⎛ 364 ⎞ √ That is, 1 − ≈ 1− ⎜ ⎟ 365 ⎠ 365 n1 ⎝ n2 Therefore, 1 − 365 × 364 × ... × ( 365 − n1 + 1) ⎛ 364 ⎞ ≈ 1− ⎜ ⎟ n1 365 ⎝ 365 ⎠ n C 21 NUS/FOS/DSAP Lecture 12 – 10 GEM2900 - Understanding Uncertainty & Statistical Thinking Semester 2, 2010/2011 How to Calculate with Probabilities 3 couples attend a dance class where the instructor pairs everyone off at random. Matching Problem What is the probability that at least one couple gets to pair together? = 1 – P(no match) P(at least one match) G1 B1 B1 B2 B2 B3 B3 G2 B2 B3 B1 B3 B1 B2 G3 B3 B2 B3 B1 B2 B1 NUS/FOS/DSAP Lecture 12 – 11 GEM2900 - Understanding Uncertainty & Statistical Thinking Semester 2, 2010/2011 How to Calculate with Probabilities 3 couples attend a dance class where the instructor pairs everyone off at random. Matching Problem Wh...
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This note was uploaded on 05/19/2011 for the course STAT 2900 taught by Professor Chenpeiyi during the Spring '11 term at National University of Singapore.

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