you are dealt five cards sequentially numbered 1,2,3,4, and 5 from a shuffled deck. let E_i denote the event that the i^th card dealt is even numbered. That is, E_1 denotes the event that the first card drawn is even numbered.

a. What is P(E_2|E_1), the probability that the second card is even given that the first card is even?

b. Let O_i represent the event that the i^th card dealt is odd numbered. What is P(E_2|o1), the conditional probability that the second card is even given that the first card is odd?

c. what is the conditional probability that the second card is odd given that the first card is even?

d. what is the conditional probability that the first two care are even given that the third card is even?