Question

let a and b be two events with the following probabilities. the probability that a occurs is 0.5. the probability that b occurs is 0.3. the probability that a occurs given that b occurs is 0.8. what is the conditional probability that b occurs given that a occurs? write your answer as a decimal. do not round.

Explanation:

Step1: Use the formula for conditional probability

The formula for conditional probability is \(P(A|B)=\frac{P(A\cap B)}{P(B)}\). We know \(P(A|B) = 0.8\) and \(P(B)=0.3\). So, \(P(A\cap B)=P(A|B)\times P(B)\).

$$P(A\cap B)=0.8\times0.3 = 0.24$$

Step2: Use another formula for conditional probability

The formula \(P(B|A)=\frac{P(A\cap B)}{P(A)}\). We know \(P(A\cap B) = 0.24\) and \(P(A)=0.5\).

$$P(B|A)=\frac{0.24}{0.5}=0.48$$

Answer:

\(0.48\)