Question

question 11 of 25
a and b are independent events.
p(a) = 0.50
p(b) = 0.20
what is p(a|b)?
a. 0.50
b. not enough information
c. 0.10
d. 0.20

Explanation:

Step1: Recall the formula for conditional probability

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

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

\(P(A|B)=\frac{P(A)\times P(B)}{P(B)}\)

Step4: Simplify the expression

Since \(P(B)
eq0\) (here \(P(B) = 0.20\)), \(\frac{P(A)\times P(B)}{P(B)}=P(A)\)

Step5: Substitute the value of \(P(A)\)

Given \(P(A)=0.50\), so \(P(A|B)=0.50\)

Answer:

A. 0.50