Question

Consider 6 different-color marbles that are randomly selected. Create a scenario for event A
𝐴
and a scenario for event B
𝐵
, such that P(A and B)=130
𝑃
(
𝐴

and

𝐵
)
=
1
30
. State the result of event A
𝐴
, the result of event B
𝐵
, and explain if the two events are independent or dependent.(4 points) simple

Answer 1

Let the marbles be 6 different colors. Draw two marbles one after the other without replacement.

- Event A: the first marble is red. Then P(A) = 1/6.
- Event B: the second marble is blue. Without any other information P(B) = 1/6.

P(A and B) = P(first is red AND second is blue) = (1/6)·(1/5) = 1/30.

Check independence: if A and B were independent we would have P(A and B) = P(A)·P(B) = (1/6)·(1/6) = 1/36, but 1/30 ≠ 1/36. Also P(B|A) = 1/5 ≠ P(B) = 1/6. Therefore A and B are dependent.