Question

question 5
3 pts
if a and b are independent events with p(a)=0.45 and p(b)=0.73 calculate and find p(a|b)=?
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

For any two events \(A\) and \(B\), the formula for conditional probability 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 \(P(A\cap B) = P(A)\times P(B)\). Substituting this into the conditional - probability formula, we get \(P(A|B)=\frac{P(A)\times P(B)}{P(B)}\).

Step3: Simplify the expression

Since \(P(B)
eq0\) (because \(P(B) = 0.73\)), we can cancel out \(P(B)\) in the numerator and the denominator. So \(P(A|B)=P(A)\).

Answer:

\(0.45\)