CD-player plays random tracks from random CDs. Suppose that

[dts5044]

A CD player has a magazine that holds six Cds. The machine is capable of randomly selecting a CD at random and then selecting a song randomly from that CD. Suppose that five CDs are albums by Paul McCartney and one is by Billy Joel. The player selects songs until a song by Billy Joel is played after which the maching is turned off. Give the probability that the machine is turned of after:

a) the sixth song

equivalent to 5 times having paul mccartney and then having billy joel. i.e. (5/6)^5 * 1/6

b) at least five songs have been played.

equivalent to all possible outcomes after having paul mccartney play 4 times. i.e. (5/6)^4

c) suppose now that the songs continue to be played until the second song by Billy Joel has been played. Find the probability that at most four songs are played.

this is 1 - the probability of having at least five songs having been played. the probability of at least 5 songs being played is: ?

 

[pka]

Re: discrete distribution probability

Have you answered part (b) of the question correctly?
Is that question opposite of this: “What is the probability the process ends in the first four plays”?

 

[dts5044]

Re: discrete distribution probability

yes part (b) is correct,

and no part (c) is not the opposite of part b because there is the new criteria that the player turns off after the second billy joel song instead of the first, so you can't just take P( x <= 4) = (1 - (b))

 

[dts5044]

Re: discrete distribution probability

never mind i figured it out.

 

[pka]

Re: discrete distribution probability

never mind i figured it out.

I tried to point out to you that your answer to part b is not correct.

 

[dts5044]

Re: discrete distribution probability

could you explain why please? Because it gives the correct answer according to the back of the book; am I getting the right answer using the wrong method?

 

[pka]

Re: discrete distribution probability

could you explain why please? Because it gives the correct answer according to the back of the book; am I getting the right answer using the wrong method?

“Backs of books” are notoriously wrong. Graduate students are paid $x per problem to solve them. They could careless about correctness. I know because I was one of those some years ago. Then you were fired only if your error rate exceeded 15%.

You gave the answer for the process to end in exactly five plays.
But the question says at least five.
Now that means that the termination occurs at 5, 6, 7, …, whatever.