Knowee
Questions
Features
Study Tools

A radio disc jockey has 7 songs on this upcoming hour's playlist: 3 are rock songs, 2 are reggae songs, and 2 are country songs. The disc jockey randomly chooses the first song to play, and then she randomly chooses the second song from the remaining ones. What is the probability that both songs are country songs? Write your answer as a fraction in simplest form.

Question

A radio disc jockey has 7 songs on this upcoming hour's playlist: 3 are rock songs, 2 are reggae songs, and 2 are country songs. The disc jockey randomly chooses the first song to play, and then she randomly chooses the second song from the remaining ones. What is the probability that both songs are country songs? Write your answer as a fraction in simplest form.

🧐 Not the exact question you are looking for?Go ask a question

Solution

To solve this problem, we need to understand that the probability of both songs being country songs is the product of the probability of the first song being a country song and the probability of the second song being a country song, given that the first song was a country song.

Step 1: Calculate the probability of the first song being a country song. There are 2 country songs out of a total of 7 songs, so the probability is 2/7.

Step 2: If the first song is a country song, there is now 1 country song left out of a total of 6 remaining songs. So, the probability of the second song being a country song, given that the first song was a country song, is 1/6.

Step 3: Multiply the two probabilities together to get the overall probability of both songs being country songs.

So, the probability is (2/7) * (1/6) = 2/42 = 1/21.

Therefore, the probability that both songs are country songs is 1/21.

This problem has been solved

Similar Questions

For a few weeks, a music producer kept track of newly released songs on a music streaming website. She recorded the music genre and number of times the song was played on its release date.0-500 plays 501-1,000 playsCountry 7 7Rock 3 2What is the probability that a randomly selected song had 501-1,000 plays given that the song was country?Simplify any fractions.

You are a DJ at a wedding. A playlist contains 10 pop songs and 20 country songs. You set the playlist to select songs at random. Once a song is played, the same song will not play again. Find the probability that the first two songs to play are both country songs. Express your first answer as a fraction in simplest form, and round your percent answer to the nearest tenth. The probability is , or about %.

For a few weeks, a music producer kept track of newly released songs on a music streaming website. He recorded the music genre and number of times the song was played on its release date.The probability that a song was pop is 0.09, the probability that it had 501-1,000 plays is 0.58, and the probability that it was pop or had 501-1,000 plays is 0.64.What is the probability that a randomly chosen song was pop and had 501-1,000 plays?Write your answer as a whole number, decimal, or simplified fraction.

A disc jockey at a school dance has equal numbers of rock and country songs that she randomly selects from. She designs a simulation to estimate the probability that the next three songs she plays are all country songs.Which simulation design could she use to estimate the probability?A.Number cubeLet 1 = rockLet 2 = countryRoll cube three times. Repeat.B.Number cubeLet even number = rockLet odd number = countryRoll cube three times. Repeat.C.Random digitsLet 1, 2, 3 = rockLet 4, 5, 6 = countrySelect three random digits. Repeat.D.Random digitsLet 1, 2, 3, 4, 5 = rockLet 6, 7, 8, 9 = countrySelect three random digits. Repeat.SUBMITarrow_backPREVIOUS

An album has 15 songs. You make a playlist by randomly shuffling the order of the songs. Which values represent the probability that the first 3 songs in the playlist are the first 3 songs on the album in any order?Responses$\frac{1}{_{15}C_3}$115​C3​​​the fraction with numerator 1 and denominator 15 cap c sub 3$\frac{1}{_{15}P_3}$115​P3​​​the fraction with numerator 1 and denominator 15 cap p sub 3$\frac{1}{455}$1455​​1 over 455$\frac{1}{2730}$12730​​

1/2

Upgrade your grade with Knowee

Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.