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. what is the probability that a randomly selected song had 501 - 1,000 plays given that the song was country? simplify 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. what is the probability that a randomly selected song had 501 - 1,000 plays given that the song was country? simplify any fractions.

Answer

Explanation:

Step1: Recall conditional - probability formula

The formula for conditional probability is $P(A|B)=\frac{P(A\cap B)}{P(B)}$. In terms of counts, if we let $A$ be the event of having 501 - 1000 plays and $B$ be the event of being a country song, then $P(A|B)=\frac{n(A\cap B)}{n(B)}$, where $n(A\cap B)$ is the number of country songs with 501 - 1000 plays and $n(B)$ is the total number of country songs.

Step2: Identify relevant values from the table

From the table, the number of country songs with 501 - 1000 plays, $n(A\cap B)=5$. The total number of country songs, $n(B)=3 + 5=8$.

Step3: Calculate the probability

$P(A|B)=\frac{5}{8}$

Answer:

$\frac{5}{8}$