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Question

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.
Country Rock
0 times a week 2 4
1-2 times a week 2 2
What is the probability that a randomly selected student sings in the shower 0 times a week and prefers rock?
Simplify any fractions.

Answer 1

To find the probability that a randomly selected student sings in the shower 0 times a week and prefers rock, we first need to determine the total number of students and the number of students who fit the criteria.

From the data provided:

• For Country music:

  • 0 times a week: 2 students
  • 1-2 times a week: 2 students
  • Total Country music students: \(2 + 2 = 4\)

• For Rock music:

  • 0 times a week: 4 students
  • 1-2 times a week: 2 students
  • Total Rock music students: \(4 + 2 = 6\)

Now we can find the total number of students surveyed: \[ \text{Total students} = \text{Total Country} + \text{Total Rock} = 4 + 6 = 10 \]

Next, we need to determine how many students sing in the shower 0 times a week and prefer rock. According to the data:

• Number of students who prefer rock and sing 0 times a week: 4 students

Now we can calculate the probability: \[ P(\text{sings 0 times a week and prefers rock}) = \frac{\text{Number of students who sing 0 times and prefer rock}}{\text{Total number of students}} = \frac{4}{10} \]

Now we simplify the fraction: \[ \frac{4}{10} = \frac{2}{5} \]

Thus, the probability that a randomly selected student sings in the shower 0 times a week and prefers rock is \(\boxed{\frac{2}{5}}\).