Question

9. A poll was taken of 13,507 working adults aged 40-70 to determine their level of education. The participants were classified by sex and by level of education. The results are shown below.Education LevelMaleFemaleTotalHigh School or Less368231266808Bachelor's Degree226236545916Master's Degree360304664Ph.D.4970119Total6353715413,507A person is selected at random. Compute the following probabilities.(a) What is the probability that the selected person is male, given that he has a Master's degree? (b) What is the probability that the selected person does not have a Master's degree, given that he is male? (c) What is the probability that the selected person is female, given that she has a Bachelor's degree? (d) What is the probability that the selected person has a Ph.D., given that she is female?

Answer 1

Conditional probability formula: Probability of A given B:

`P(A|B)=(P(A\cap B))/(P(B))`

a) What is the probability that the selected person is male (M), given that he has a Master's degree (MD)?

`\begin{gathered} P(M|MD)=(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)=(360)/(664)\approx0.54 \end{gathered}`

b) What is the probability that the selected person does not have a Master's degree (NMD), given that he is male (M)?

`\begin{gathered} P(MD|M)=(P(NMD\cap M))/(P(M)) \\ \\ P(MD|M)=\frac{\#males-\#\text{males with master degr}ee}{\#males} \\ \\ P(MD|M)=(6353-360)/(6353)=(5993)/(6353)\approx0.94 \end{gathered}`

c) What is the probability that the selected person is female (F), given that she has a Bachelor's degree (BD)?

`\begin{gathered} P(F|BD)=(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)=(3654)/(5916)\approx0.62 \end{gathered}`

d)What is the probability that the selected person has a Ph.D (PH)., given that she is female (F)?

`\begin{gathered} P(PH|F)=(P(PH\cap F))/(P(F)) \\ \\ P(PH|F)=\frac{\#\text{females with Ph.D}}{\#Females} \\ \\ P(PH|F)=(70)/(7154)\approx0.0098 \end{gathered}`