Hi there!

Here's a problem from a problem set on probability I haven't had a chance to solve on time. Would appreciate any help

Tim has 30 albums of 10 songs each on his iPhone, and he listens to a total of 12 songs on shuffle

every morning before classes begin. Each of the 300 songs is equally likely to be chosen, although a

song is never selected more than once.one of the 30 albums, Neil Diamond's The Jazz Singer, is Tim's absolute favorite.

a. (5 points) Compute Px(X) which defines the number of songs x that just so happen to be from

his favorite album.

Answer.

b. (5 points) What is the probability there are two or more songs from the same album (not nec-

essarily his favorite) are among the 12 selected?

c. (5 points) If Tim hears one particular song (The First Time Ever I Saw Your Face, Roberta

Flack) in the shuffle, it makes him so sad that he stops listening immediately, even if fewer

than 12 songs have played. Given this new piece of information, what is the expected number

of songs Tim listens to?

Thank you!!