Question

determine the conditional - probability. write the answer as a fraction or decimal.
given (p(a)=\frac{1}{4}), (p(b)=\frac{1}{3}), and (p(a and b)=\frac{1}{6}), determine (p(a|b)).

1. enter the answer in the input provided. use numbers instead of words.

(p(a|b)=)

Explanation:

Step1: Recall the formula for conditional probability

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

Step2: Substitute the given values

We are given that $P(A\cap B)=\frac{1}{16}$ and $P(B)=\frac{1}{8}$. Substituting these values into the formula, we get $P(A|B)=\frac{\frac{1}{16}}{\frac{1}{8}}$.

Step3: Simplify the expression

$\frac{\frac{1}{16}}{\frac{1}{8}}=\frac{1}{16}\times\frac{8}{1}=\frac{1}{2}$.

Answer:

$\frac{1}{2}$