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Chapter 4: Problem 52

Given that \(P(B \mid A)=.70\) and \(P(A\) and \(B)=.35\), find \(P(A)\).

Short Answer

Expert verified
The probability of event A, \(P(A)\), is 0.5.

Step by step solution

01

Identify the Known Values

In this problem, the known values are the conditional probability of B given A, which is denoted as \(P(B \mid A)=.70\), and the joint probability of A and B, which is denoted as \(P(A \cap B)=.35\).
02

Use the Formula for Conditional Probability

The formula for conditional probability can be rearranged to solve for \(P(A)\). It becomes \(P(A) = P(A \cap B) / P(B \mid A)\).
03

Substitute the Known Values into the Formula

Substitute \(P(B \mid A)=.70\) and \(P(A \cap B)=.35\) into the formula to get \(P(A) = .35 / .70\).
04

Solve for P(A)

Doing the division, we find that \(P(A) = .35 / .70 = 0.5\).

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