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    Can someone help me with these please?

    The three events A, B and C are defined in the same sample space. The events A and C are
    mutually exclusive. The events A and B are independent.

    Given that P(A) = 2/5, P(C) = 1/3 and P(A U B ) = 5/8 find


    (a) P(A U C),

    (b) P(B).

    (Do i draw 3 circles?)
    The events A and B are independent with P(A) = 1/2 and P(A U B) = 2/3
    Find
    (a) P(B),

    (b) P(A|B),

    (c) P(B'|A).

    (I don't get this mutually exclusive and Independent stuff )
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    (Original post by Jonario)
    Can someone help me with these please?

    The three events A, B and C are defined in the same sample space. The events A and C are
    mutually exclusive. The events A and B are independent.

    Given that P(A) = 2/5, P(C) = 1/3 or P(A U B ) = 5/8 find


    (a) P(A U C),

    (b) P(B).

    (Do i draw 3 circles?)
    The events A and B are independent with P(A) = 1/2 and P(A U B) = 2/3
    Find
    (a) P(B),

    (b) P(A|B),

    (c) P(B'|A).

    (I don't get this mutually exclusive and Independent stuff )
    I am not sure how to help without just giving the answers, but anyway

    P(AUC)= probability of BOTH A and C occuring which is 1/3+2/5

    We know

    P(AUB)=P(A)+P(B) -P(AnB)

    but as A and B are independent then P(AnB)=P(A)P(B)

    so solving for P(B) we get

    5/8= 2/5 + P(B) -p(B)2/5
    so P(B)=3/8

    For the second question we have:

    (a), to find P(B) follow the same process as I have in the previous question, noting A and B are independent.

    (b) For conditional probability just use the formula

    (c) Do you mean B' is the complement or?
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    (Original post by zcomputer5)
    I am not sure how to help without just giving the answers, but anyway

    P(AUC)= probability of BOTH A and C occuring which is 1/3+2/5

    We know

    P(AUB)=P(A)+P(B) -P(AnB)

    but as A and B are independent then P(AnB)=P(A)P(B)

    so solving for P(B) we get

    5/8= 2/5 + P(B) -p(B)2/5
    so P(B)=9/56

    For the second question we have:

    (a), to find P(B) follow the same process as I have in the previous question, noting A and B are independent.

    (b) For conditional probability just use the formula

    (c) Do you mean B' is the complement or?

    5/8= 2/5 + P(B) -p(B)2/5
    so P(B)=9/56 Could you tell me how yo u got this?
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    (Original post by Jonario)
    5/8= 2/5 + P(B) -p(B)2/5
    so P(B)=9/56 Could you tell me how yo u got this?
    By making a mistake

    Actually I think all you have to do is just note P(omega)=1 thus 1=P(C) +P(A) +P(B) thought this would give you 4/15. Sorry about that, its too late for me.

    For the second question:

    P(B)= 2/3 - 1/2
    PA|B)=P(AnB)/P(B)=P(A) (as independent)
    P(B|A)= P(BnA)/P(A)=p(B) as independent
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    (Original post by zcomputer5)
    By making a mistake

    Actually I think all you have to do is just note P(omega)=1 thus 1=P(C) +P(A) +P(B) thought this would give you 4/15. Sorry about that, its too late for me.
    So.. whats the right answer?
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    (Original post by Jonario)
    So.. whats the right answer?
    4/15
 
 
 
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