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juglugjuglug
juglugjuglug asked in Science & MathematicsMathematics · 6 years ago

If E and F are events for which P(E union F)=1 then P(E' union F')=?

A) 0

B) P(E')+P(F')-P(E')P(F')

C) P(E')+P(F')

D) P(E')+P(F')-1

E) 1

1 Answer

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  • Samwise
    Lv 7
    6 years ago
    Favorite Answer

    P(E') + P(F') is correct (answer C)

    The more general answer would be the one given by the inclusion-exclusion principle:

    P(E') + P(F') - P(E' ∩ F')

    where P(E' ∩ F') is subtracted to avoid double-counting.

    But in this case, we've been informed that

    P(E ∪ F) = 1

    which means that

    P(E' ∩ F') = 0

    This is one of many examples where it helps to remember there are 4 basic cases:

    E ∩ F

    E' ∩ F

    E ∩ F'

    E' ∩ F'

    E ∪ F = (E ∩ F) ∪ (E' ∩ F) ∪ (E ∩ F')

    That is, it's the composition of the basic cases except E' ∩ F'.

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