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According to the general equation for conditional probability, if P(AB) =

4/5
and P(B) = 5/6, what is P(AIB)?
A.15/16
B.35/36
C.8/9
D.24/25

User Cleggy
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1 Answer

6 votes

Answer:


\sf D. \quad P(A|B)=(24)/(25)

Explanation:

General equation for conditional probability


\sf P(A \cap B)=P(A)\:P(B|A)

As we need to find P(A|B) we can rewrite the equation:


\implies \sf P(B \cap A)=P(B)\:P(A|B)

Given:


\sf P(A \cap B)=(4)/(5)


\sf P(B)=(5)/(6)

Remember that
\sf P(A \cap B)=P(B \cap A)

Substitute the given values into the formula:


\implies \sf P(B \cap A)=P(B)\:P(A|B)


\implies \sf (4)/(5)=(5)/(6)\:P(A|B)


\implies \sf P(A|B)=(4)/(5) / (5)/(6)


\implies \sf P(A|B)=(4)/(5) * (6)/(5)


\implies \sf P(A|B)=(24)/(25)

User Mario Tacke
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