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if E and F are independent events, find P(F) if P(E)=0.2 and P(E U F)= 0.3

  • math -

    If F and E are independent events then P(E and F) = 0
    and we also know
    P(E or F) = P(E) + P(F) - P(E and F)
    .3 = .2 + P(F) - 0
    P(F) = .1

  • math -

    Let P(F)= X
    since E and F are independent eveents,
    P(EnF)= P(E)* P(F)
    therefore, P(EnF)= 0.2X
    but P(EuF)=P(E)+ P(F)- P(EnF)
    0.3= 0.2 + x - 0.2x
    x = 1/8

  • math -

    sorry, i made a mistake, for mutually exculsive events, P(EnF)= 0, hence,
    from the previous equation,
    0.3=0.2+P(F)-0
    so P(F)= 0.1

  • Medical Physics -

    Independent does not mean mutually exclusive, thus

    P(EUF)=P(E)+P(F)-P(EnF)

    Independence allows us to write:

    P(EUF)=P(E)+P(F)-P(E)P(F)
    P(EUF)=P(E)+[1-P(E)]P(F)

    Therefore,

    P(F)= [P(EUF)-P(E)]/[1-P(E)]

    P(F)=[0.3-0.2]/[1-0.2]
    =.1/.8
    =1/8

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