You draw 2 cards from a standard deck of cards without replacement.
a.) what is the probability that the first card is an ace OR the second card is a clubs.
b.) what is the probability that the first card is an ace AND the second card is a clubs
The Attempt at a Solution
a.) I thought there were 2 cases to consider: your first card could be any of 3 aces that are not the club (3/52 probability) and you add to that the probability of drawing a club on your second draw (13/51). the other case is drawing the ace of clubs (probability 1/52) and adding to it the probability of drawing a club on the second try(12/51). So in all I have (3/52)+(13/51)+(1/52)+(12/51) which is a probability higher than 1/2 and it seems wrong.
b.) Same thing except this time i multiplied:
due to my suspicious answer for part (a) I suspect (b) is also wrong. I do not have the answer sheet.