Question

let a and b be two events with the following probabilities.

• ( p(a)=0.8 )
• ( p(b)=0.6 )
• ( p(a \text{ and } b)=0.24 )

what is the conditional probability of b given a?
write your answer as a decimal. do not round.

Explanation:

Step1: Recall the formula for conditional probability

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

Step2: Substitute the given values into the formula

We are given that \(P(A) = 0.8\) and \(P(A\cap B)=0.24\). Substituting these values into the formula, we get \(P(B|A)=\frac{0.24}{0.8}\).

Step3: Calculate the value

\(\frac{0.24}{0.8}=0.3\)

Answer:

\(0.3\)