From an ordinary deck of 52 cards we draw cards at random, with replacement, and successively until an ace is drawn. What is the probability that it takes an even number of draws to get the first spade?

From an ordinary deck of 52 cards we draw cards at random, with replacement, and successively until an ace is drawn. What is the probability that it takes an even number of draws to get the first spade?

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Question

Is my solution to my problem correct? If not explain where I went wrong.

From an ordinary deck of 52 cards we draw cards at random, with replacement, and successively until an ace is drawn. What
is the probability that it takes an even number of draws to get the first spade?
PCX=2) + P (X=4) + P(X+6) + ... =P (Even #)
(²12) (²2²) + ( 2 ) (6₂)² + (32)(82)
48
485
Geo series
12,3
( 13 ) ( 13 ) + (1 3) ( 13² )² + (1 3) (+) ³ +...
S = 12/164 - 1²/3
12
1/13
a=
f=ts
12
169

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