Question

6. A poll was taken of 14,502 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 Less361831176735Bachelor's Degree286037626622Master's Degree5744761050Ph.D.415495Total7093740914,502A person is selected at random. Compute the following probabilities.(a) What is the probability that the selected person does not have a Ph.D.? (b) What is the probability that the selected person does not have a Master's degree? (c) What is the probability that the selected person is female or has a Master's degree? (d) What is the probability that the selected person is male or has a Ph.D.?

Answer 1

From the table,

The total number of persons, n(s)=14,502.

a)

To find the probability that the selected person does not have a Ph.D.

The number of persons does not have a Ph.D is,

`\begin{gathered} n\mleft(A\mright)=6735+6622+1050 \\ n(A)=14407 \end{gathered}`

So, the probability is,

`\begin{gathered} P(A)=(n(A))/(n(s)) \\ =(14407)/(14502) \end{gathered}`

Hence, the answer is,

`(14407)/(14502)`

b) To find the probability that the selected person does not have a Master's degree

The number of person does not have a Master's degree is,

`\begin{gathered} n\mleft(B\mright)=6735+6622+95 \\ n(B)=13452 \end{gathered}`

So, the probability is,

`\begin{gathered} P(B)=(n(B))/(n(s)) \\ =(13452)/(14502) \\ =(2242)/(2417) \end{gathered}`

Hence, the answer is,

`(2242)/(2417)`

c)

To find the probability that the selected person is female or has a Master's degree

Let n(C) be the number of females.

Let n(D) be the number of persons have master's degree.

Let n(CnD) be the number of persons who both female and have master's degree.

Using the formula,

`P(C\cup D)=P(C)+P(D)-P(C\cap D)`

So,