Use the verb diagram to calculate conditional probabilities Which conditional probabilities are correct? Check all that apply. P(D|F)=6/34 P(E|D)=7/25 P(D|E)=7/25 P(F|E)=8/18 P(…

Question

asked Sep 16, 2020 185k views

1 Answer

Life Evader · Answer 1 · 2020-09-20T23:14:21+0000

The Venn diagram explicitly tells us that the universe consists of 60 objects, and

$P(D\cap E\cap F)=\frac1{60}$

$P(D\cap E)=(1+6)/(60)=\frac7{60}$

$P(D\cap F)=(1+5)/(60)=\frac1{10}$

$P(E\cap F)=(1+7)/(60)=\frac2{15}$

$P(D)=(13+6+5+1)/(60)=\frac5{12}$

$P(E)=(4+6+7+1)/(60)=\frac3{10}$

P(F)=(21+5+7+1)/(60)=(17)/(30)

$P(D\cup E\cup F)=1-\frac3{60}=(19)/(20)$

By definition of conditional probability, we have

$P(D\mid F)=(P(D\cap F))/(P(F))=\frac{\frac1{10}}{(17)/(30)}=\frac3{17}$

$P(E\mid D)=\frac{\frac7{60}}{\frac5{12}}=\frac7{25}$ (only this one is correct)

$P(D\mid E)=\frac{\frac7{60}}{\frac3{10}}=\frac7{18}$

$P(F\mid E)=\frac{\frac2{15}}{\frac3{10}}=\frac49$

$P(E\mid F)=\frac{\frac2{15}}{(17)/(30)}=\frac4{17}$