Question

use the following probabilities to answer the question. round to 4 decimal places.
$p(a)=0.53, p(b)=0.42, p(a \text{ and } b)=0.05$
$p(b|a)=$

Explanation:

Step1: Recall conditional - probability formula

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

Step2: Substitute given values

We are given that $P(A) = 0.53$ and $P(A\ and\ B)=0.05$. Substituting these values into the formula, we get $P(B|A)=\frac{0.05}{0.53}$.

Step3: Calculate the result

$P(B|A)=\frac{0.05}{0.53}\approx0.0943$

Answer:

$0.0943$