# Question: using a standard deck of 52 cards consisting of 13...

###### Question details

Using a standard deck of 52 cards, consisting of 13 spades, 13
hearts, 13 diamonds, and 13 clubs. I am

interested in seeing how many non-heart cards I can draw before
picking a heart. After each draw,

I will put the card back in the deck, so there is a 1/4 chance I
get a heart with each draw, and a 3/4

chance I do not get a heart. I think about this a little bit and
come up with the following probability

model for X, the number of non-hearts drawn before I get a
heart.

(a) Using the fact that the probability space must have a total
measure of one, find the value of c.

(Yes, I know there is another way to find c directly from the
experiment description, but I want you to

use/remember this important infinite series. Of course, the answer
you get should be consistent with

what you would expect from the experiment.)

(b) Find

(c) Find {0, 2,
4, 6, ...} )