ANSWER
[tex]P(B \: and \: C) = \frac{1}{6}[/tex]
EXPLANATION
Recall that,
[tex]P(A \: and \: B)=P(A) \times P(B)[/tex]
But we were given that,
[tex]P(A)= \frac{1}{8} [/tex]
and
[tex]P(A \: and \: B) = \frac{1}{12} [/tex]
We substitute these values into the above formula to obtain,
[tex] \frac{1}{12} = \frac{1}{8} \times P(B)[/tex]
This implies that,
[tex] \frac{1}{12} \times 8=8 \times \frac{1}{8} \times P(B)[/tex]
This simplifies to,
[tex] P(B) = \frac{8}{12} [/tex]
[tex] P(B) = \frac{2}{3} [/tex]
So we can now find
[tex]P(B \: and \: C).[/tex]
We use the same formula again,
[tex]P(B \: and \: C) = P(B) \times P(C)[/tex]
We substitute the values to get,
[tex]P(B \: and \: C) = \frac{2}{3} \times \frac{1}{4} [/tex]
We multiply out to get,
[tex]P(B \: and \: C) = \frac{1}{6}[/tex]
