Question

determine the conditional probability. write the answer as a fraction or decimal.
given (p(a)=\frac{1}{3}), (p(b)=\frac{1}{4}), and (p(acap b)=\frac{1}{12}), determine (p(b|a)).
enter the answer in the space provided. use numbers instead of words.
(p(b|a)=)

Explanation:

Step1: Recall Bayes' theorem

$P(B|A)=\frac{P(A\cap B)}{P(A)}$

Step2: Substitute given values

We are given $P(A)=\frac{1}{4}$, $P(A\cap B)=\frac{1}{16}$. Substituting into the formula: $P(B|A)=\frac{\frac{1}{16}}{\frac{1}{4}}$.

Step3: Simplify the fraction

$\frac{\frac{1}{16}}{\frac{1}{4}}=\frac{1}{16}\times4=\frac{1}{4}$

Answer:

$\frac{1}{4}$