Question

determine the conditional - probability. write the answer as a fraction or decimal.
given (p(a)=\frac{1}{2}), (p(b)=\frac{1}{3}), and (p(a and b)=\frac{1}{6}), determine (p(b|a)).

• enter the answer in the space provided. use numbers instead of words.

(p(b|a)=square)

Explanation:

Step1: Recall the formula for conditional probability

The formula for conditional probability is $P(B|A)=\frac{P(A\cap B)}{P(A)}$.

Step2: Substitute the given values

We are given that $P(A)=\frac{1}{3}$, and $P(A\cap B)=\frac{1}{6}$. Substituting these values into the formula, we get $P(B|A)=\frac{\frac{1}{6}}{\frac{1}{3}}$.

Step3: Simplify the fraction

$\frac{\frac{1}{6}}{\frac{1}{3}}=\frac{1}{6}\times\frac{3}{1}=\frac{1}{2}$.

Answer:

$\frac{1}{2}$