Question

Current Attempt in Progress Suppose that $P(A \mid B)=0.2, P\left(A \mid B{prime}right)=0.4$, and $P(B)=0.6$. What is the $P(A)$ ? Round your answer to two decimal places (e.g. 98.76). SP.AS. 1004

Answer 1

To find P(A), we can use the law of total probability. According to the law of total probability, P(A) = P(A | B)P(B) + P(A | B')P(B'). Substituting the given values, we get P(A) = (0.2)(0.6) + (0.4)(0.4) = 0.12 + 0.16 = 0.28.

Step-by-step explanation:

In this question, we are given that:

• P(A | B) = 0.2
• P(A | B') = 0.4
• P(B) = 0.6

We are asked to find P(A).

To find P(A), we can use the law of total probability. According to the law of total probability, P(A) = P(A | B)P(B) + P(A | B')P(B').

Substituting the given values, we get P(A) = (0.2)(0.6) + (0.4)(0.4) = 0.12 + 0.16 = 0.28.

Therefore, P(A) = 0.28.