Question

question 4 3 pts if ( p(a)=0.42 ) and ( p(b)=0.61 ), and ( p(a cup b)=0.74 ), 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: Use the formula for \(P(A\cup B)\)

We know that \(P(A\cup B)=P(A)+P(B)-P(A\cap B)\).
Substituting the given values: \(0.74 = 0.42+0.61 - P(A\cap B)\).
Then, \(P(A\cap B)=0.42 + 0.61-0.74\).

$$P(A\cap B)=0.29$$

Step2: Use the formula for conditional probability

The formula for conditional probability is \(P(A|B)=\frac{P(A\cap B)}{P(B)}\).
Substitute \(P(A\cap B) = 0.29\) and \(P(B)=0.61\) into the formula: \(P(A|B)=\frac{0.29}{0.61}\).

$$P(A|B)\approx0.4754$$

Answer:

\(0.4754\)