Question

given the following venn diagram: data a 0.36 0.29 b 0.17 0.18 note: when answering the questions below, if any final answer that needs to be rounded, use your rounded value when finding the answer. for any answers with more than two decimal places, write your final answer to four decimal places. a. calculate the probability p(a|b)=? b. calculate the probability p(b|a)=?

Explanation:

Step1: Recall the formula for conditional probability

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

Step2: Identify \(P(A\cap B)\) and \(P(B)\) from the Venn - diagram

From the Venn - diagram, \(P(A\cap B) = 0.29\) and \(P(B)=0.29 + 0.17=0.46\).

Step3: Calculate \(P(A|B)\)

Substitute the values into the formula: \(P(A|B)=\frac{0.29}{0.46}\approx0.63\).

Step4: Recall the formula for \(P(B|A)\)

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

Step5: Identify \(P(A\cap B)\) and \(P(A)\) from the Venn - diagram

From the Venn - diagram, \(P(A\cap B) = 0.29\) and \(P(A)=0.29+0.36 = 0.65\).

Step6: Calculate \(P(B|A)\)

Substitute the values into the formula: \(P(B|A)=\frac{0.29}{0.65}\approx0.45\).

Answer:

\(P(A|B)\approx0.63\), \(P(B|A)\approx0.45\)