Probability
Conditional Probability
Grade 12
Question:
<p>If $$P(A) = \frac{3}{8}$$, $$P(B) = \frac{3}{8}$$ and $$P(A \cap B) = \frac{1}{4}$$, then $$P\left(\frac{A}{B}\right)$$ is equal to</p>
<p>(a) $$\frac{1}{4}$$</p>
<p>(b) $$\frac{1}{3}$$</p>
<p>(c) $$\frac{2}{3}$$</p>
<p>(d) $$\frac{3}{4}$$</p>
Step-by-Step Solution
Key Concept: Apply the conditional probability formula and simplify the fraction correctly.
Using the formula for conditional probability:
$$P\left(\frac{A}{B}\right) = \frac{P(A \cap B)}{P(B)}$$
Given $P(A \cap B) = \frac{1}{4}$ and $P(B) = \frac{3}{8}$.
Substitute these values into the formula:
$$P\left(\frac{A}{B}\right) = \frac{\frac{1}{4}}{\frac{3}{8}}$$
$$P\left(\frac{A}{B}\right) = \frac{1}{4} \times \frac{8}{3}$$
$$P\left(\frac{A}{B}\right) = \frac{8}{12}$$
$$P\left(\frac{A}{B}\right) = \frac{2}{3}$$
Correct Answer: B