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# 7 Proportions - Proportions A proportion is the fraction of...

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Proportions A proportion is the fraction of individuals having a particular attribute. Example: 2092 adult passengers on the Titanic; 654 survived Proportion of survivors = 654/2092 ! 0.3 Probability that two out of three randomly chosen passengers survived the Titanic

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Binomial distribution The binomial distribution describes the probability of a given number of " successes " from a fixed number of independent trials. n trials; p probability of success Pr[ X ] = n X ! # % & p X 1 p ( ) n X n X ! # % & = n ! X ! n X ( ) ! 6! = 6 5 4 3 2 1 = 720 0!=1 1!=1 n! = n n-1 n-2 ... 3 2 1 ! Probability that two out of three randomly chosen passengers survived the Titanic Pr[2] = 3 2 ! # % & 0.3 ( ) 2 1 0.3 ( ) 3 2 = 3! 2! ( 1! 0.3 ( ) 2 0.7 ( ) 1 = 3 0.3 ( ) 2 0.7 ( ) = 0.189
Probability that two out of three randomly chosen passengers survived the Titanic Pr[2] = 3 2 ! # % & 0.3 ( ) 2 1 0.3 ( ) 3 2 Number of ways to get 2 survivors out of 3 passengers ! Probability of 2 survivors ! Probability of 1 death ! Example: Paradise flycatchers A population of paradise flycatchers has 80% brown males and 20% white. Your field assistant captures 5 male flycatchers at random. What is the chance that 3 of those are brown and 2 are white?

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7 Proportions - Proportions A proportion is the fraction of...

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