Thread: Probability, distribution and covariance with a deck of 52 cards

Here is my problem,

Start with a standard, uniformly shued 52-card deck, and draw the cards one at a
time.

(a) What is the probability of drawing a King strictly before getting a Spade?
(b) What is the distribution of the number of Jacks drawn after the last Queen is drawn?
(c) Let X1 be the position at which the 1rst Spade is drawn, and X2 the position at which the 1rst Club is drawn. Calculate the distribution of X1.

For (a), I tried by conditionning probability, combinatory and a long sum of probability which gave me 3/16 but my solution is really too long so I don't think I'm using the shortest method here. Do you have any shortcut?

For (b) I don't understand quietly how to find the distribution?

For (c) of course there is a covariance because drawing one or the other will have an influence on the position of the next card, but how to calculate such a covariance.

Thank you

Originally Posted by solvj

Here is my problem,

Start with a standard, uniformly shued 52-card deck, and draw the cards one at a
time.

(a) What is the probability of drawing a King strictly before getting a Spade?
(b) What is the distribution of the number of Jacks drawn after the last Queen is drawn?
(c) Let X1 be the position at which the 1rst Spade is drawn, and X2 the position at which the 1rst Club is drawn. Calculate the distribution of X1.

For (a), I tried by conditionning probability, combinatory and a long sum of probability which gave me 3/16 but my solution is really too long so I don't think I'm using the shortest method here. Do you have any shortcut?

For (b) I don't understand quietly how to find the distribution?

For (c) of course there is a covariance because drawing one or the other will have an influence on the position of the next card, but how to calculate such a covariance.

Thank you

a) There are 13 spades and 4 kings, one of the kings is the king of spades. There are 16 cards to worry about. Of these 16 cards you win if one of the 3 non-spade kings is first. Does that help ?

b) Here there are 8 cards to worry about and you are looking at how the sequence ends. You want to know the probability of it ending:

Q - no jacks drawn after the last queen
QJ - one drawn
QJJ - two
QJJJ- three
JJJJ - four

c) why are you calculating the covariance ? I don't understand how you are approaching this problem.