Question

question 7 of 10
a and b are independent events.
p(a) = 0.30
p(b) = 0.40
what is p(a|b)?
a. 0.30
b. 0.40
c. 0.12
d. not enough information

Explanation:

Step1: Recall the formula for conditional probability

For any two events \(A\) and \(B\), the conditional - probability formula is \(P(A|B)=\frac{P(A\cap B)}{P(B)}\).

Step2: Use the property of independent events

If \(A\) and \(B\) are independent events, then \(P(A\cap B)=P(A)\times P(B)\).

Step3: Substitute into the conditional - probability formula

Substitute \(P(A\cap B) = P(A)\times P(B)\) into \(P(A|B)=\frac{P(A\cap B)}{P(B)}\). We get \(P(A|B)=\frac{P(A)\times P(B)}{P(B)}\).
Since \(P(B)=0.40
eq0\), we can cancel out \(P(B)\) in the numerator and the denominator.
So \(P(A|B)=P(A)\).
Given \(P(A) = 0.30\), then \(P(A|B)=0.30\).

Answer:

A. 0.30