This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
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You're on a roll — 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 Cancer | Male | Female | Total | |---|---|---|---| | A | 57 | 39 | 57 + 39 = 96 | | B | 42 | 62 | 42 + 62 = 104 | | Total | 57 + 42 = 99 | 39 + 62 = 101 | 96 + 104 = 200 | The total number of individuals is 200. i) Find the probability that the selected individual is a male. Step 1: Identify the number of males. From the table, the total number of male individuals is 99. Step 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 Individuals P(Male) = (99)/(200) The probability that the selected individual is a male is (99)/(200). ii) Find the probability that the selected individual is a type A cancer. Step 1: Identify the number of type A cancer patients. From the table, the total number of individuals with type A cancer is 96. Step 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 Individuals P(Type A) = (96)/(200) Step 3: Simplify the fraction. Both the numerator and the denominator are divisible by 8. P(Type A) = (96 ÷ 8)/(200 ÷ 8) = (12)/(25) The probability that the selected individual is a type A cancer is (12)/(25). What's next?