Question

the probability of event a occurring is 0.27, the probability of event b occurring is 0.19, and the probability of events a and b occurring is 0.05. determine 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 into the formula

We are given that \(P(A\cap B) = 0.05\) and \(P(B)=0.19\). Substituting these values into the formula, we get \(P(A|B)=\frac{0.05}{0.19}\).

Step3: Calculate the value

\(\frac{0.05}{0.19}\approx0.263\)

Answer:

\(0.263\)