Conditional probability formula: Probability of A given B:
[tex]P(A|B)=\frac{P(A\cap B)}{P(B)}[/tex]
a) What is the probability that the selected person is male (M), given that he has a Master's degree (MD)?
[tex]\begin{gathered} P(M|MD)=\frac{P(M\cap MD)}{P(MD)} \\ \\ P(M|MD)=\frac{\#\text{males with a master degre}e}{\#\text{ persons with master degre}e} \\ \\ P(M|MD)=\frac{360}{664}\approx0.54 \end{gathered}[/tex]
b) What is the probability that the selected person does not have a Master's degree (NMD), given that he is male (M)?
[tex]\begin{gathered} P(MD|M)=\frac{P(NMD\cap M)}{P(M)} \\ \\ P(MD|M)=\frac{\#males-\#\text{males with master degr}ee}{\#males} \\ \\ P(MD|M)=\frac{6353-360}{6353}=\frac{5993}{6353}\approx0.94 \end{gathered}[/tex]
c) What is the probability that the selected person is female (F), given that she has a Bachelor's degree (BD)?
[tex]\begin{gathered} P(F|BD)=\frac{P(F\cap BD)}{P(BD)} \\ \\ P(F|BD)=\frac{\#\text{females with Bachelor degre}e}{\#persons\text{ with bachelord degre}e} \\ \\ P(F|BD)=\frac{3654}{5916}\approx0.62 \end{gathered}[/tex]
d)What is the probability that the selected person has a Ph.D (PH)., given that she is female (F)?
[tex]\begin{gathered} P(PH|F)=\frac{P(PH\cap F)}{P(F)} \\ \\ P(PH|F)=\frac{\#\text{females with Ph.D}}{\#Females} \\ \\ P(PH|F)=\frac{70}{7154}\approx0.0098 \end{gathered}[/tex]
