Question

I take a standard deck of 52 cards, consisting of 13 spades, 13 hearts, 13 diamonds, and 13 clubs. I am interesting 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 ofc. (Yes, I know there is another way to find e 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 є {0, 2, 4. 6, . . .).

Answer 1