Question

Thomas selects one of the garments at random. Let A be the event that he selects a blue garment and let B be the event that he chooses a shirt. Which of the following statements are true?

(A) P(A|B)=P(A)
(B) P(B|A)=P(B)
(C) Events A and B are independent events.
(D) The outcome of events A and B are dependent on each other.
(E) P(A and B)=P(A)⋅P(B)

Answer 1

We need more information to determine if A and B are independent.

Step-by-step explanation:

The events A and B are independent if the following conditions are true:

1. P(AB) = P(A)
2. P(B|A) = P(B)
3. P(A and B) = P(A)P(B)

From the given information, we know that P(A) is the probability of selecting a blue garment, and P(B) is the probability of selecting a shirt. In order to determine if A and B are independent, we need to compare P(A and B) with P(A)P(B).

To find P(A and B), we need more information about the probability of selecting a blue shirt. Without this information, we cannot determine if A and B are independent.