91影视

What percentage of the original class attended the party?

Consider events:

S - a randomly chosen person from the class attends the success party.

M -a randomly chosen person from the class is male

F - a randomly chosen person from the class is female

Given probabilities ( conditioned on being in the class)

$P_c(S鈭�F)=0.48$

$P_c(S鈭�M)=0.37$

$P_c\left(M\right)=0.62$

Men and women are considered competing hypothesis so:

$F=M^c鈬�P_c\left(F\right)=1鈭�P_c\left(M\right)=38\mathrm{\%}$

$\text{Use the version of Bayes formula (obtained by breaking}S\text{into}SM\text{and}SF\text{)}$

$P_c\left(S\right)=P\left(M\right)P(S鈭�M)+P\left(F\right)P(S鈭�F)$

$=0.62鈰�0.37+0.38鈰�0.48$

=$0.4118$

The percentage of the original class attended the party is$0.4118$

what percentage of those attending the party were women?

$\text{Therefore, the answer to b) is}41.18\%\text{of people from the class attended the success party.}$

$P_c(F鈭�S)=\frac{P_c\left(FS\right)}{P_c\left(S\right)}$

$=\frac{P_c(S鈭�F)P_c\left(F\right)}{P_c\left(S\right)}$

$=\frac{0.48鈰�0.38}{0.4118}$

$=0.4429$

percentage of those attending the party were women is$0.4429$