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Math Help - Easy Probability

  1. #1
    Member Mr Rayon's Avatar
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    Easy Probability

    If Pr(A) = 4 Pr(B), Pr(A\cup B) =0.8 and Pr(A\cap B) = 0.2, find:
    a) Pr(B)
    b) Pr(A)

    The bit that confuses me most was probably "Pr(A) = 4 Pr(B)" in the question above. Is this a typo? I've tried figuring this out for few times but I keep getting negative numbers.

    Any help would be appreciated.
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  2. #2
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    Recall that P(A\cup B)=P(A)+P(B)-P(A\cap B)
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  3. #3
    Member Mr Rayon's Avatar
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    Yeah, I used that formula, just rearranged but kept getting negative numbers, ignoring Pr(B) in the question and assuming it was a typo.
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  4. #4
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    0.8 = 5P(B) - 0.2\, \Rightarrow \,5P(B) = 1

    Where is there a negative?
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  5. #5
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    Hello, Mr Rayon!

    \text{If }\text{Pr}(A) = 4\!\cdot\!\text{Pr}(B),\;\;\text{Pr}(A\cup B) = 0.8,\;\;\text{Pr}(A\cap B) = 0.2

    \text{Find: }\,\text{Pr}(A)\,\text{ and }\,\text{Pr}(B)

    That first equation says: . \text{Pr}(A) is four times \text{Pr}(B).


    Formula: . \text{Pr}(A \cup B) \;=\;\text{Pr}(A) + \text{Pr}(B) - \text{Pr}(A \cap B)

    Substitute: . . . 0.8 \quad\;= \;4\!\cdot\!\text{Pr}(B) + \text{Pr}(B) \;\;- \;\; 0.2

    So we have: . 1.0 \;=\;5\!\cdot\!\text{Pr}(B) \quad\Rightarrow\quad \boxed{\text{Pr}(B) \,=\,0.2}

    Then: . \text{Pr}(A) \:=\:4\!\cdot\!\text{Pr}(B) \;=\;4(0.2) \quad\Rightarrow\quad \boxed{\text{Pr}(A)\;=\;0.8}
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