for a few weeks, a music producer kept track of newly released songs on a music streaming website. he…

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.\n| |0 - 500 plays|501 - 1,000 plays|\n|--|--|--|\n|country|3|5|\n|rock|5|4|\n|pop|6|4|\nwhat is the probability that a randomly selected song had 501 - 1,000 plays given that the song was country?\nsimplify any fractions.

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.\n| |0 - 500 plays|501 - 1,000 plays|\n|--|--|--|\n|country|3|5|\n|rock|5|4|\n|pop|6|4|\nwhat is the probability that a randomly selected song had 501 - 1,000 plays given that the song was country?\nsimplify any fractions.

Answer

Answer:

$\frac{5}{8}$

Explanation:

Step1: Find total country - songs

The total number of country songs is the sum of country songs in each play - range. So, $3 + 5=8$.

Step2: Identify favorable cases

The number of country songs with 501 - 1000 plays is 5.

Step3: Calculate conditional probability

The formula for conditional probability $P(A|B)=\frac{P(A\cap B)}{P(B)}$. In the case of frequency data, if $A$ is the event of having 501 - 1000 plays and $B$ is the event of being a country song, the probability that a song has 501 - 1000 plays given it is a country song is $\frac{\text{Number of country songs with 501 - 1000 plays}}{\text{Total number of country songs}}=\frac{5}{8}$.