Suppose you draw a single card from a standard deck of 52 playing cards.
a. What is the probability that this card is a diamond or a club?
b. What is the probability that this card is not a 4?
c. Given that this card is a black card, what is the probability that it is a spade?
d. Let E_1 be the event that this card is a black card. Let E_2 be the event that this card is a spade. Are E_1 and E_2 independent events? Why or why not?
e. Let E_3 be the event that this card is a heart. Let E_4 be the event that this card is a 3. Are E_3 and E_4 independent events? Why or why not?