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Definition of conditional probability:
P(A|B)=P(A^B)/P(B)

In this case, B is replaced by B', so
P(A|B')=P(A^B')/P(B')=(1/6)/(7/12)=2/7
JeanaShupp

Answer: [tex]P(A|B')=\dfrac{2}{7}[/tex]

Step-by-step explanation:

  • The general equation for conditional probability :

[tex]P(M|N)=\dfrac{P(M\cap N)}{P(N)}[/tex]

Given :  P(A∩B') = 1/6 and P(B')= 7/12

According to the general equation for conditional probability, we have

[tex]P(A|B')=\dfrac{P(A\cap B')}{P(B')}\\\\\Rightarrow\ P(A|B')=\dfrac{\dfrac{1}{6}}{\dfrac{7}{12}}\\\\\Rightarrow\ P(A|B')=\dfrac{1}{6}\times\dfrac{12}{7}\\\\\Rightarrow\ P(A|B')=\dfrac{2}{7}[/tex]

Hence, [tex]P(A|B')=\dfrac{2}{7}[/tex]

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