Solve the following problem:
A random experiment consists of drawing a ball from an urn that contains 4 red balls numbered 1, 2, 3, 4 and three black balls numbered 1, 2, 3.
The following events are defined.
1. E1 = The number on the ball is even.
2. E2 = The color of the ball is red, and its number is greater than 1.
3. E3 = The number on the ball is less than 3.
4. E4 = E1 ∪ E3
5. E5 = E1 ∪ (E2 ∩ E3)
Answer the following questions.
1. What is P(E2)?
2. What is P(E3|E2)?
3. What is P(E2|E4E3)?
4. Are E3 and E5 independent?