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14 December, 07:15

Suppose P (E) = 0.15, P (F) = 0.65, and P (F | E) = 0.82, compute the following:

P (E and F). P (E or F). P (E | F).

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  1. 14 December, 07:40
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    P (E and F) = 0.123

    P (E or F) = 0.677

    P (E|F) = 0.189

    Step-by-step explanation:

    The formula for conditional probability is P (B|A) = P (A and B) / P (A)

    The addition rule is P (A or B) = P (A) + P (B) - P (A and B)

    ∵ P (E) = 0.15

    ∵ P (F) = 0.65

    ∵ P (F|E) = 0.82

    - Use the first rule above

    ∵ P (F|E) = P (E and F) / P (E)

    - Substitute the values of P (F|E) and P (E) to find P (E and F)

    ∴ 0.82 = P (E and F) / 0.15

    - Multiply both sides by 0.15

    ∴ 0.123 = P (E and F)

    - Switch the two sides

    ∴ P (E and F) = 0.123

    Use the second rule to find P (E or F)

    ∵ P (E or F) = P (E) + P (F) - P (E and F)

    ∴ P (E or F) = 0.15 + 0.65 - 0.123

    ∴ P (E or F) = 0.677

    Use the first rule to find P (E|F)

    ∵ P (E|F) = P (F and E) / P (F)

    - P (F and E) is the same with P (E and F)

    ∴ P (E|F) = 0.123/0.65

    ∴ P (E|F) = 0.189
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