Question

question 2
3 pts
if a and b are independent events with ( p(a)=0.13 ) and ( p(b)=0.51 ) calculate and find ( p(b | a)=? )
note: if your final answer has up to four decimal places, enter your answer in the box below without rounding it. but if your final answer has more than four decimal places, then round the number to four decimal places.

Explanation:

Step1: Recall the formula for conditional probability

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

Step2: Use the property of independent events

For independent events \(A\) and \(B\), \(P(A\cap B)=P(A)\times P(B)\).
So \(P(B|A)=\frac{P(A)\times P(B)}{P(A)}\).

Step3: Simplify the expression

Cancel out \(P(A)\) in the numerator and denominator. We get \(P(B|A) = P(B)\).

Answer:

\(0.51\)