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Math Help - Probability Q Again..

  1. #1
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    Probability Q Again..

    The number showing on the upper faces when two fair six-sided dice are tossed is observed. Consider events A and B defined as:
    A - the total score is at least 8
    B - at least one die achieves a score of 2 or less

    Find
    1. P(B') (in 3 dec pl)
    2. P(A or B) ( in 3 dec pl)

    Thanks
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  2. #2
    MHF Contributor red_dog's Avatar
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    1) We have 36 possible cases and 12 favourable cases: (1,1), (1,2), (1,2), (1,4), (1,5), (1,6), (2,1), (2,2), (2,3), (2,4), (2,5), (2,6).
    So \displaystyle P(B)=\frac{12}{36}=\frac{1}{3}.

    2) P(A\cup B)=P(A)+P(B)-P(A\cap B).
    For P(A): we have 15 favourable cases, so \displaystyle P(A)=\frac{15}{36}=\frac{5}{12}
    For P(A\cap B) we have 2 favourable cases, so P(A\cap B)=\displaystyle\frac{2}{36}=\frac{1}{18}.
    Then P(A\cup B)=\displaystyle\frac{5}{12}+\frac{1}{3}-\frac{1}{18}
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