Question

Let A and B denote random events. Suppose P(A) = 0.45, P(B) = 0.63, and P(A and B) = 0.27. What is P(B|A)? a) 0.45 b) 0.63 c) 0.27 d) 0.60

Answer 1

To find P(B|A), use the formula P(B|A) = P(A and B) / P(A) and substitute the given values.

Step-by-step explanation:

To find P(B|A), we can use the formula for conditional probability:

P(B|A) = P(A and B) / P(A)

Given that P(A) = 0.45, P(B) = 0.63, and P(A and B) = 0.27, we can substitute these values into the formula:

P(B|A) = 0.27 / 0.45 = 0.6

Therefore, the answer is d) 0.60.

Answer 2

The correct answer is the conditional probability of event B given event A, P(B|A), which is calculated using the formula P(A and B) / P(A). Using the provided probabilities, P(B|A) is determined to be 0.60.

Step-by-step explanation:

The student is asking about the concept of conditional probability, specifically they need to find the probability of event B given that event A has occurred, which is denoted as P(B|A). The formula to calculate this is P(B|A) = P(A and B) / P(A).

Given that P(A) = 0.45, P(B) = 0.63, and P(A and B) = 0.27, we plug these values into the formula to find P(B|A).

So, P(B|A) = P(A and B) / P(A) = 0.27 / 0.45.

Now performing the division we get:

P(B|A) = 0.6.

The answer to the student's question is option d) 0.60.