Question

Please answer the question ​

Answer 1

Answer: 0.45

Step-by-step explanation:

From the given table, the total number of students = 137

The number of students are sophomores =35+42=77

Let A be the event that students are sophomores.

Then probability that students are sophomores is given by  :

$\text{P(A)}=\dfrac{77}{137}$

The number of sophomores who attended the jazz concert = 35

Let B be the event that students attended the jazz concert .

The probability that students attended the jazz concert and are sophomores is given by  :

$\text{P(A and B)}=\dfrac{35}{137}$

Now, the probability of that the student attended the jazz concert, given that the students is sophomore is given by :-

$P(B|A)=\dfrac{\text{P(A and B)}}{\text{P(A)}}\\\\=\dfrac{\dfrac{35}{137}}{\dfrac{77}{137}}\\\\\\=\dfrac{35}{77}=0.454545454545\approx0.45$

Answer 2

Answer: 0.45

Step-by-step explanation:

From the given table, the total number of students = 137

The number of students are sophomores =35+42=77

Let A be the event that students are sophomores.

Then probability that students are sophomores is given by  :

The number of sophomores who attended the jazz concert = 35

Let B be the event that students attended the jazz concert .

The probability that students attended the jazz concert and are sophomores is given by  :

Now, the probability of that the student attended the jazz concert, given that the students is sophomore is given by :-