on the first day of music class, students submitted a survey. one survey question asked students to report…

on the first day of music class, students submitted a survey. one survey question asked students to report which music genre they prefer. another question asked students how frequently they sing in the shower.\n| |0 times a week|1 - 2 times a week|\n|--|--|--|\n|country|4|5|\n|rock|5|4|\nwhat is the probability that a randomly selected student prefers country given that the student sings in the shower 1 - 2 times a week?\nsimplify any fractions.

on the first day of music class, students submitted a survey. one survey question asked students to report which music genre they prefer. another question asked students how frequently they sing in the shower.\n| |0 times a week|1 - 2 times a week|\n|--|--|--|\n|country|4|5|\n|rock|5|4|\nwhat is the probability that a randomly selected student prefers country given that the student sings in the shower 1 - 2 times a week?\nsimplify any fractions.

Answer

Explanation:

Step1: Identify relevant values

We want $P(\text{Country}|\text{1 - 2 times a week})$. The number of students who sing 1 - 2 times a week and prefer country is 5. The total number of students who sing 1 - 2 times a week is $5 + 4=9$.

Step2: Apply conditional - probability formula

The formula for conditional probability $P(A|B)=\frac{P(A\cap B)}{P(B)}$. In terms of counts, $P(\text{Country}|\text{1 - 2 times a week})=\frac{\text{Number of (Country and 1 - 2 times a week)}}{\text{Number of (1 - 2 times a week)}}$. So the probability is $\frac{5}{9}$.

Answer:

$\frac{5}{9}$