Louis inserts a 12 track cd into the cd player

[wind]

Hi can someone please check my work?

Louis inserts a 12 track cd into the cd player and pressed the random play button. This CD player's random function choses each track independently of the previous track played.

a) what is the probability that the cd player will select Louis's favorite track first

so if this is a geometric dist. right?

q=11/12
p=1/12
x=0

\(\displaystyle \L\ P(x)=q^xp\)

\(\displaystyle \L\
P(x)=\frac{11}{12}^0\frac{1}{12}\)

\(\displaystyle \L\ P(x)=\frac{1}{12}\)

b)what is the probability that the second selected tract is not his favorite

\(\displaystyle \L\
P(x)=\frac{11}{12}^2\frac{1}{12}^0\)

\(\displaystyle \L\ P(x)=0.840277778\)

c) what is the expected waiting time before his favorite is played

E(x)=q/p

\(\displaystyle \L\
E(x)=\frac{\frac{11}{12}}{\frac{1}{12}}\)

E(x)=11

d) If Louis have 2 favorite tracts, what is the expected wating time before he hears both?

p= 2/12
q= 10/12

E(x)= 5

*******

thanks

 

[pka]

See my other answer to understand this one.
\(\displaystyle \L 12\left( {1 + \frac{1}{2} + \frac{1}{3} + \cdots + \frac{1}{12}} \right)\).
This is the wait-time until all 12 are played.