Question

Consider a situation in which P(A) = 1/8, P(C) = 1/4, and P(A and B) = 1/12. What is P(B and C)?

Answer 1

ANSWER

$P(B \: and \: C) = \frac{1}{6}$


EXPLANATION

Recall that,

$P(A \: and \: B)=P(A) \times P(B)$

But we were given that,

$P(A)= \frac{1}{8}$

and

$P(A \: and \: B) = \frac{1}{12}$


We substitute these values into the above formula to obtain,


$\frac{1}{12} = \frac{1}{8} \times P(B)$



This implies that,

$\frac{1}{12} \times 8=8 \times \frac{1}{8} \times P(B)$



This simplifies to,

$P(B) = \frac{8}{12}$


$P(B) = \frac{2}{3}$


So we can now find
$P(B \: and \: C).$



We use the same formula again,

$P(B \: and \: C) = P(B) \times P(C)$
We substitute the values to get,


$P(B \: and \: C) = \frac{2}{3} \times \frac{1}{4}$
We multiply out to get,


$P(B \: and \: C) = \frac{1}{6}$

Answer 2

Answer:

1/6

Step-by-step explanation: