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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.
P(X = n) = c(rac{3}{4})^n , n = 0, 1, 2, ...
(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 P(X 2 2)

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

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