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A study of 200 patients with two types of cancer, A and B, found the following distribution by gender. Calculate the probabilities for the given events.

Mathematics

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2 parts
i

99200\frac{99}{200}

ii

1225\frac{12}{25}

Step-by-step solution

5 steps

here's the solution for question 6.

First, let's complete the table by summing the rows and columns to find the total number of patients.

Type of CancerMaleFemaleTotal
A573957+39=9657 + 39 = 96
B426242+62=10442 + 62 = 104
Total57+42=9957 + 42 = 9939+62=10139 + 62 = 10196+104=20096 + 104 = 200

The total number of individuals is 200.

Part i· 2 steps

Find the probability that the selected individual is a male.

  1. Identify the number of males.

    From the table, the total number of male individuals is 99.

  2. Calculate the probability.

    The probability of selecting a male is the number of males divided by the total number of individuals.

    P(Male)=Number of MalesTotal Number of IndividualsP(\text{Male}) = \frac{\text{Number of Males}}{\text{Total Number of Individuals}} P(Male)=99200P(\text{Male}) = \frac{99}{200}

    The probability that the selected individual is a male is 99200\boxed{\frac{99}{200}}.

Part ii

1225\frac{12}{25}

Find the probability that the selected individual is a type A cancer.

  1. Identify the number of type A cancer patients.

    From the table, the total number of individuals with type A cancer is 96.

  2. Calculate the probability.

    The probability of selecting an individual with type A cancer is the number of type A cancer patients divided by the total number of individuals.

    P(Type A)=Number of Type A Cancer PatientsTotal Number of IndividualsP(\text{Type A}) = \frac{\text{Number of Type A Cancer Patients}}{\text{Total Number of Individuals}} P(Type A)=96200P(\text{Type A}) = \frac{96}{200}

  3. Simplify the fraction.

    Both the numerator and the denominator are divisible by 8.

    P(Type A)=96÷8200÷8=1225P(\text{Type A}) = \frac{96 \div 8}{200 \div 8} = \frac{12}{25}

    The probability that the selected individual is a type A cancer is 1225\boxed{\frac{12}{25}}.

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