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I am given some questions and I need help.

(1)You are dealt two cards from a pack of 52 cards. What is the conditional probability that

(a) both of them are aces if at least one of them is the ace of spades?

(b) both of them are aces if at least one of them is an ace?

a) I know that the probability of being dealt 2 aces out of 2 cards is : (4x3)/(52x52)=1/221

there are 6 possible ways to arrange the aces and 3 to have Ace of spades. So should it be just 1/221/2 ?

This is the conditional probability of being dealt 2 aces out of 2 cards, right?

P(A1A2)=P(A1)P(A2|A1)=P(A2|A1)=P(A1A2)/P(A1) , but what should I change to get the condition right?

b)Isnt it P(A2|A1)/P(A1)?

And I don't have idea about the 2nd one:

(2) Consider a pack of 52 cards.

(a), What is the probability that there is a king right after the first ace?

(b), What is the probability that there is an ace right after the first ace?

(c) What is the probability that the 1st ace is the 30-th card?

(d) If the 1st ace is the 30-th card, what is the conditional probability the next card is the ace of spades?

(e) If the 1st ace is the 30-th card, what is the conditional probability the next card is

the jack of diamonds?

Note that you have to give these probabilities without looking at any cards from the pack.

a) if the Ace is the first card it gives 4/52 and the king is right after the ace is 4/51, but what when they are not 1st and 2nd cards

b) is almost the same 4/52*3/51 ?

c) I have no idea what is the correct approach, but I think since there are 22 cards left we should have 4/52 - 4/22?

I have no Idea on the last 2.

Thanks a lot!