SOLUTION: Please help me solve this in simple way. Thank You. Determine all joint probabilities listed below from the following information: P(A)=0.73,P(Ac)=0.27,P(B|A)=0.56,P(B|Ac)=0.

Question 1119951: Please help me solve this in simple way. Thank You.
Determine all joint probabilities listed below from the following information:
P(A)=0.73,P(Ac)=0.27,P(B|A)=0.56,P(B|Ac)=0.69
P(A and B) =
P(A and Bc) =
P(Ac and B) =
P(Ac and Bc)
Answer by greenestamps(13203) (Show Source): You can put this solution on YOUR website!

By definition, P(B|A) = (P(A and B))/(P(A))

Think of the conditional probability as having only A as the sample space (so P(A) is the denominator of the probability fraction); you want to know what percentage of A is also B.

So for the first question,

P(A and B) = (P(A))*(P(B|A)) = .73*.56 = .4088.

For the second question,

P(A and not B) = P(A) - P(A and B) = .73 - .4088 = .3212.

For the third question, again we have, by definition,

P(B| not A) = (P(B and not A))/(P(not A)), so

P(B and not A) = (P(B| not A))*(P(not A)) = .69*.27 = .1863.

For the fourth question, P(not A and not B) is "all that is left":

1 - (.4088+.3212+.1863) = .0837.
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