Respuesta :
Option C
Answer:
According to the general equation for conditional probability, If [tex]P(A \cap B)=\frac{1}{6}[/tex] and P(B) = [tex]\frac{7}{18}[/tex] then [tex]\mathrm{P}(\mathrm{A} | \mathrm{B})=\frac{3}{7}[/tex]
Solution:
Given that [tex]P(A \cap B)=\frac{1}{6}[/tex] and [tex]\mathrm{P}(\mathrm{B})=\frac{7}{18}[/tex]
We have to find the value of [tex]\mathrm{P}(\mathrm{A} | \mathrm{B})[/tex]
We know that [tex]P(A | B)=\frac{P(A \cap B)}{P(B)}[/tex]
In order to find the value of [tex]P(A | B)[/tex] substitute the value [tex](A \cap B) \text { and } P(B)[/tex] from the given data.
Step 1:
[tex]P(A | B)=\frac{P(A \cap B)}{P(B)}[/tex]
[tex]P(A | B)=\frac{\frac{1}{6}}{\frac{7}{18}}[/tex]
Step 2:
By evaluating the above term we get below expression
[tex]\begin{array}{l}{\mathrm{P}(\mathrm{A} | \mathrm{B})=\frac{1}{6} \times \frac{18}{7}} \\ {\mathrm{P}(\mathrm{A} | \mathrm{B})=\frac{3}{7}}\end{array}[/tex]
Hence we found the value for [tex]\mathbf{P}(\mathbf{A} | \mathbf{B})=\frac{3}{7}[/tex] using the given data.
