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A population of 500 graduate professionals consists of employed and unemployed bankers and accountants. There are 120 employed bankers, 40 unemployed bankers, 80 employed accountants, and 260 unemploy

Mathematics

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a)

  1. Calculate the total number of Graduate Professionals.

    Total number of Graduate Professionals = Number of Employed Bankers + Number of Unemployed Bankers + Number of Employed Accountants + Number of Unemployed Accountants
    Total = 120+40+80+260=500120 + 40 + 80 + 260 = 500

    a) (i) Calculate the probability that the chosen Graduate is an Employed Accountant.
    Number of Employed Accountants = 80

    P(Employed Accountant)=Number of Employed AccountantsTotal number of Graduate ProfessionalsP(\text{Employed Accountant}) = \frac{\text{Number of Employed Accountants}}{\text{Total number of Graduate Professionals}} P(Employed Accountant)=80500P(\text{Employed Accountant}) = \frac{80}{500} P(Employed Accountant)=850P(\text{Employed Accountant}) = \frac{8}{50} P(Employed Accountant)=425P(\text{Employed Accountant}) = \frac{4}{25} P(Employed Accountant)=0.16P(\text{Employed Accountant}) = 0.16

    The probability that the chosen Graduate is an Employed Accountant is 425 or 0.16\boxed{\frac{4}{25} \text{ or } 0.16}.

    a) (ii) Calculate the probability that the chosen Graduate is an Unemployed Banker.
    Number of Unemployed Bankers = 40

    P(Unemployed Banker)=Number of Unemployed BankersTotal number of Graduate ProfessionalsP(\text{Unemployed Banker}) = \frac{\text{Number of Unemployed Bankers}}{\text{Total number of Graduate Professionals}} P(Unemployed Banker)=40500P(\text{Unemployed Banker}) = \frac{40}{500} P(Unemployed Banker)=450P(\text{Unemployed Banker}) = \frac{4}{50} P(Unemployed Banker)=225P(\text{Unemployed Banker}) = \frac{2}{25} P(Unemployed Banker)=0.08P(\text{Unemployed Banker}) = 0.08

    The probability that the chosen Graduate is an Unemployed Banker is 225 or 0.08\boxed{\frac{2}{25} \text{ or } 0.08}.

    b)

  2. Identify the total number of employees.

    Total number of employees = 150

  3. Determine the number of workers who are either male or female.

    In a company, all workers are either male or female. Therefore, the number of workers who are either male or female is equal to the total number of employees.
    Number of workers (male or female) = 150

  4. Calculate the probability.

    P(male or female worker)=Number of workers (male or female)Total number of employeesP(\text{male or female worker}) = \frac{\text{Number of workers (male or female)}}{\text{Total number of employees}} P(male or female worker)=150150P(\text{male or female worker}) = \frac{150}{150} P(male or female worker)=1P(\text{male or female worker}) = 1

    The probability of selecting a worker who is either a male or female worker is 1\boxed{1}.

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