Question

determine the conditional probability. write the answer as a fraction or decimal.
given (p(a)=0.25), (p(b) = 0.3), and (p(acap b)=0.1), determine (p(a|b)).

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

(p(a|b)=)

Explanation:

Step1: Recall conditional - probability formula

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

Step2: Substitute given values

We are given that $P(A\cap B) = 0.1$ and $P(B)=0.3$. Substituting these values into the formula, we get $P(A|B)=\frac{0.1}{0.3}$.

Step3: Simplify the fraction

$\frac{0.1}{0.3}=\frac{1}{3}\approx0.333$.

Answer:

$\frac{1}{3}$ or $0.333$