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you are given the probabilities listed below P(A)= 0.25, P(B) = 0.30, P(C)=0.55, P(A&C) = 0.05, P(B&C)=0, P(B/A)=0.48.

A) ARE A AND B INDEPENDENT?
B) FIND P(A&B)
C) FIND P(A OR B)
D) FIND P(A/B)
E) ARE B AND C MUTUALLY EXCLUSIVE EVENTS?
F) ARE B AND C INDEPENDENT EVENTS?

  • stats -

    A) A and B are not independent: P(A)*P(B)= 0.25*0.30 = 0.075. This is not equal to P(A and B) = P(B|A)*P(A) = 0.48*0.25 = 0.12.
    B) P(A and B) = P(B|A)*P(A) = 0.48*0.25 = 0.12.
    C) P(A or B) = P(A) + P(B) - P(A and B) = 0.25 + 0.30 - 0.12 = 0.43

    D) P(A|B) = P(A and B)/P(B) = 0.12/0.30 = 0.40
    E) B and C are mutually exclusive, because it is given that P(B and C)=0 (Definition of mutual exclusivity.)
    F) P(B)*P(C) = 0.30*0.55 = 0.165
    P(B and C) = 0
    ==> The two quantities are not equal, hence B and C are not independent.

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