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Prove that if E and F are independent ev...

Prove that if E and F are independent events, then so are the events E and F'.

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A die is throuwn. If E is the event the number appearing is a multiple of 3 and F be the event the number appearing is even then prove that E and F are independent events.

An unbiased die is thrown twice. Let the event A be 'odd number on the first throw' and B the event 'odd number on the second throw'. Check the independence of the events A and B.

Knowledge Check

  • If two events are independent, then

    A
    they must be mutuallly exclusive
    B
    the sum of their probabilities must be equal
    C
    (a) and (b) both are correct
    D
    none of the above is correct

  • If events A and B are independent, then P(A cap B) =

    A
    P(A) + P(B)
    B
    P(A)_P(B)
    C
    P(A).P(B)
    D
    P(A)|P(B)

  • Two events A and B will be independent if

    A
    A and B are mutually exclusive
    B
    `P(A'nn B')=(1-P(A))(1-P(B))`
    C
    `P(A)-P(B)`
    D
    `P(A)+P(B)=1`

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    If A and B are independent events such that P(A) gt 0, P(B) gt 0 , then

    If bar (E )and bar(F) are complementary events of events E and F respectively and 0 lt P(F) lt 1 , then :

    Let E^(c ) denote the complement of an event E . Let E,F ,G be pair - wise independent events with P(G) gt 0 and P(E ca p F cap G) = 0 . Then P(E^(C )cap F^(C )//G) equals :

    If vecE and vecF are complementary events of events E and F respectively and 0lt P(F) lt 1 , then :

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