More cards! Consider again a standard deck of 52 cards (13 in each of 4 suits). Two cards are dealt in succession (meaning no replacement).

a) What is the probability that the first card is a queen?
b) Given that the first card was a queen, what is the probability that the second card is a seven?
c) What is the probability of being dealt a queen first followed by a seven?
d) What is the probability that both cards are greater than 7 (assuming that the ace is considered “high” or greater than 7)?

Question

More cards! Consider again a standard deck of 52 cards (13 in each of 4 suits). Two cards are dealt in succession (meaning no replacement).

a) What is the probability that the first card is a queen?
b) Given that the first card was a queen, what is the probability that the second card is a seven?
c) What is the probability of being dealt a queen first followed by a seven?
d) What is the probability that both cards are greater than 7 (assuming that the ace is considered “high” or greater than 7)?

anonymous · Answer

(a) how many queens are there in the deck? well, one per suit i.e. $4$ so the probability is $4/52=1/13$ (as there are 52 equally-likely possibilities for the 1st card)

(b) if the first card is a queen we've left only $51$ cards however we know there are still $4$ seven cards in there; the probability is therefore $7/51$. note that this is higher than $7/52$ reflecting the fact that knowing more information about the deck changes probabilities

anonymous · Answer

(c) this reflects Bayes' rule i.e. $P(A\cap B)=P(A|B)P(B)$ so the probability is therefore $1/13\cdot7/51=7/663$

anonymous · Answer

I will leave (d) as an exercise