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henblantbach
henblantbach asked in Science & MathematicsMathematics · 1 decade ago

help with probability (S1)?

Missed the lesson, and now i'm blank.

A and B are independent.

P(A) = 0.3

P(A u B) = 0.58

Show that P(B) = 0.4

---------------------------------

so i've got to : 0.28 = P(B) - P(a n b)

so i need to divide 0.28 by 0.7 to get the answer, but i cant see how i'm gonna get the 0.7.

Help if you can, thank you :-)

2 Answers

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  • Pathomaniac
    Lv 4
    1 decade ago
    Favorite Answer

    P(A u B) = P(A) + P(B) - P(A n B)

    P (A u B) = P(A) + P(B) - P(A)P(B)

    P(A u B) = P(A) + P(B)(1 - P(A))

    P(B) =[ P(A u B) - P(A) ] / [ ( 1 - P(A)) ]

    P(B) = ( .58 - .3 ) / ( 1 - .3)

    P(B) = .28 / .7

    P(B) = .4

  • ?
    Lv 4
    1 decade ago

    P(A U B) = P(A) + P(B) - P(A n B)

    As they are independent, P(A n B) = P(A) * P(B)

    so 0.58 = 0.3 + P(B) - (0.3*PB)

    so 0.28 = P(B) - 0.3PB

    now just simply factorize the P(B)

    0.28 = P(B) (1 - 0.3)

    0.28 = P(B) * 0.7

    0.4 = P(B)

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