Answer :
To determine the probability that a student attended the jazz concert given that the student is a junior, we need to use the concept of conditional probability. The steps are as follows:
1. Identify the Total Number of Juniors:
From the table, we see that the total number of juniors is 60.
2. Identify the Number of Juniors Who Attended the Jazz Band Concert:
According to the table, 36 juniors attended the jazz band concert.
3. Calculate the Conditional Probability:
The conditional probability formula is:
[tex]\[ P(\text{Jazz Band Concert} | \text{Junior}) = \frac{\text{Number of Juniors Who Attended the Jazz Band Concert}}{\text{Total Number of Juniors}} \][/tex]
Plugging in the values, we get:
[tex]\[ P(\text{Jazz Band Concert} | \text{Junior}) = \frac{36}{60} \][/tex]
4. Simplify the Probability:
[tex]\[ \frac{36}{60} = 0.6 \][/tex]
5. Round the Result to Two Decimal Places:
Since [tex]\( 0.6 \)[/tex] is already in the desired format, the answer is:
[tex]\[ 0.6 \][/tex]
So, the probability that a student attended the jazz concert given that they are a junior is [tex]\( \boxed{0.6} \)[/tex].
1. Identify the Total Number of Juniors:
From the table, we see that the total number of juniors is 60.
2. Identify the Number of Juniors Who Attended the Jazz Band Concert:
According to the table, 36 juniors attended the jazz band concert.
3. Calculate the Conditional Probability:
The conditional probability formula is:
[tex]\[ P(\text{Jazz Band Concert} | \text{Junior}) = \frac{\text{Number of Juniors Who Attended the Jazz Band Concert}}{\text{Total Number of Juniors}} \][/tex]
Plugging in the values, we get:
[tex]\[ P(\text{Jazz Band Concert} | \text{Junior}) = \frac{36}{60} \][/tex]
4. Simplify the Probability:
[tex]\[ \frac{36}{60} = 0.6 \][/tex]
5. Round the Result to Two Decimal Places:
Since [tex]\( 0.6 \)[/tex] is already in the desired format, the answer is:
[tex]\[ 0.6 \][/tex]
So, the probability that a student attended the jazz concert given that they are a junior is [tex]\( \boxed{0.6} \)[/tex].
