R ile Olasılığın Temelleri
David Robinson
Chief Data Scientist, DataCamp
fair <- rbinom(90000, 20, .5) sum(fair == 14) # [1] 3410
dbinom(14, 20, .5) * .9 # [1] 0.03326797
$$\Pr(\text{14 yazı}|\text{Adil})\cdot\Pr(\text{Adil})$$
biased <- rbinom(10000, 20, .75) sum(biased == 14) # [1] 1706
dbinom(14, 20, .75) * .1 # [1] 0.01686093
$$\Pr(\text{14 yazı}|\text{Önyargılı})\cdot\Pr(\text{Önyargılı})$$
$$\Pr(\text{Önyargılı}|\text{14 yazı})=\frac{\Pr(\text{14 yazı ve Önyargılı})}{\Pr(\text{14 yazı ve Önyargılı})+\Pr(\text{14 yazı ve Adil})}$$
$$=\frac{\Pr(\text{14 yazı}|\text{Önyargılı})\Pr(\text{Önyargılı})}{\Pr(\text{14 yazı}|\text{Önyargılı})\Pr(\text{Önyargılı}) + \Pr(\text{14 yazı}|\text{Adil})\Pr(\text{Adil})}$$
prob_14_fair <- dbinom(14, 20, .5) * .9 prob_14_biased <- dbinom(14, 20, .75) * .1 prob_14_biased / (prob_14_fair + prob_14_biased)
$$\Pr(A|B)=\frac{\Pr(B|A)\Pr(A)}{\Pr(B|A)\Pr(A) + \Pr(B|\text{değil }A)\Pr(\text{değil }A)}$$
$$A = \text{Önyargılı}$$
$$B = \text{14 yazı}$$
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