Question

Jane has stored three albums on her ipod. the first album consists of 11 songs by frank sinatra, the second album consists of 13 songs by cliff richard, including "congratulations and celebrations", and the third album consists of 8 songs by john denver. she programs the shuffle function on her ipod to randomly select 10 songs from the three albums, not repeating any of the songs. find the probability that in one run of the shuffle she will definitely listen to "congratulations and celebrations.

Answer 1

The probability calculation for the song "congratulations and celebrations" to be played on a shuffled iPod requires choosing 9 out of the remaining 31 songs after reserving a slot for this specific song, and then comparing it to all possible combinations of choosing 10 songs from the total 32 available.

Step-by-step explanation:

The question involves calculating the probability that the song "congratulations and celebrations" by Cliff Richard is chosen in one run of the shuffle on Jane's iPod. Jane has three albums with a total of 32 songs (11 by Frank Sinatra, 13 by Cliff Richard, and 8 by John Denver). If the iPod is set to randomly pick 10 songs without repeating any, we want to find the probability of a specific song being chosen. Since the shuffle will definitely choose 10 songs and one of them has to be the specified song, we're essentially choosing 9 songs from the remaining 31 songs (because one slot is reserved for "congratulations and celebrations").

To calculate the probability, we'll need to use the formula for combinations to find the number of possible ways to choose 9 songs from the remaining 31, and then we'll put this over the total number of ways to pick 10 songs from all 32. So the probability is 1 times the number of ways to choose 9 songs from 31, divided by the number of ways to choose 10 songs from 32.

The calculated probability would then provide the answer to the student's question.