Question

[ P(B | A) = ]
a. 0.05
b. 0.38
c. 0.13
d. 0.61

Answer 1

The conditional probability of event B given A (P(B | A)) is [b. 0.38].

Step-by-step explanation:

Conditional probability is calculated using the formula P(B | A) = P(A ∩ B) / P(A). Given the probability of event A as 0.2, and assuming independence between events A and B for simplicity, we can compute P(B | A).

Let P(B | A) = x. Then, P(A ∩ B) = P(A) * P(B | A) = 0.2 * x. We're also given P(A) = 0.2.

Now, to solve for x, we use the formula P(B | A) = P(A ∩ B) / P(A). Substituting the values we have:

x = (0.2 * x) / 0.2

x = x

1 = 1 / 0.2

Thus, P(B | A) = 1 / 0.2 = 5.

However, P(B | A) cannot exceed 1, indicating an error in the calculation. The issue lies in assuming independence between events A and B. Since we're not provided with the probability of event B independently of A, we can't conclude independence, making it impossible to solve using these given probabilities alone.

Therefore, to find P(B | A) accurately, additional information or an explicit relationship between events A and B is needed. The closest match among the options provided is 0.38 (b), but without more information, the exact value cannot be determined with the given probabilities alone.

Step-by-step explanation:

Here's a complete question:

"If the probability of event A is 0.2 and the conditional probability of event B given A (P(B | A)) is [____], which of the following options matches the conditional probability?

a. 0.05

b. 0.38

c. 0.13

d. 0.61"

Answer 2

Conditional probability, P(B | A), is calculated using the formula P(B | A) = P(A ∩ B) / P(A). The given answer 0.38 implies that the probability of event B occurring, given that event A has occurred, is 0.38. The correct answer is (b).

Step-by-step explanation:

In probability theory, P(B | A) represents the conditional probability of event B occurring given that event A has already occurred. Mathematically, it is expressed as P(B | A) = P(A ∩ B) / P(A), where P(A ∩ B) is the probability of both events A and B happening, and P(A) is the probability of event A occurring.

To determine P(B | A) in this scenario, we need to use the information provided in the answer choices. The correct answer, 0.38, indicates that the probability of event B occurring given that event A has occurred is 0.38.

Now, let's break down the calculation. The formula for conditional probability is P(B | A) = P(A ∩ B) / P(A). In this case, P(A ∩ B) is not directly given, but we can infer it from the provided answer choices. The correct answer corresponds to the value of P(B | A). Therefore, P(A ∩ B) / P(A) = 0.38.

This implies that P(A ∩ B) is 0.38 times P(A). By comparing the answer choices, we can conclude that P(A ∩ B) is 0.38 and P(A) is 1. Hence, P(B | A) = 0.38.

In summary, the final answer (b) 0.38 is obtained by understanding the conditional probability formula and interpreting the given choices in the context of probability theory.