Assuming you are listening to your favorite playlist that has 83 country songs, but your mom also added 9 pop. Suppose that shuffle mode is on - a song played is being selected at random (with replacement) from the playlist. Find the probability that, out of the next 13 songs, at most one will be pop song.

Question

Assuming you are listening to your favorite playlist that has 83 country songs, but your mom also added 9 pop. Suppose that shuffle mode is on - a song played is being selected at random (with replacement) from the playlist. Find the probability that, out of the next 13 songs, at most one will be pop song.

Answer 1

P(pop) = 9/92

so,
P(0 pop) = (83/92)^13
P(1 pop) = 13C1 (9/92)(83/92)^12
add them up

Answer 2

@steve,

Please I'm not clear with what you mean by 13C1. Thanks

Answer 3

I got it now. 13 combination 1. Thanks

Answer 4

To find the probability that, out of the next 13 songs, at most one will be a pop song, we need to calculate the probability of two different scenarios: none of the next 13 songs being a pop song, and exactly one of the next 13 songs being a pop song. We can then sum up these probabilities to get the final result.

First, let's calculate the probability of none of the next 13 songs being a pop song:
The total number of songs in the playlist is 83 (country) + 9 (pop) = 92.
The probability of selecting a non-pop song is 83/92 for each song.

Since we are selecting songs with replacement (meaning after selecting a song, it goes back into the playlist), the probability of none of the next 13 songs being a pop song can be calculated using the probability of selecting a non-pop song for each of the 13 songs in a row:
(83/92) * (83/92) * ... * (83/92) (13 times)

Next, let's calculate the probability of exactly one of the next 13 songs being a pop song:
The probability of selecting a pop song is 9/92 for each song.

Similarly, the probability of exactly one of the next 13 songs being a pop song can be calculated using the probability of selecting a pop song for one of the 13 songs and a non-pop song for the rest (12 songs) in any order:
(9/92) * (83/92) * (83/92) * ... * (83/92) (12 times)

To find the at most one pop song probability, we add the two calculated probabilities together:
P(at most one pop song) = P(none of the next 13 songs being a pop song) + P(exactly one of the next 13 songs being a pop song)

I will now calculate the probability based on the given information.