Answer: B. 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 :
[tex]\text{P(A)}=\dfrac{77}{137}[/tex]
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 :
[tex]\text{P(A and B)}=\dfrac{35}{137}[/tex]
Now, the probability of that the student attended the jazz concert, given that the students is sophomore is given by :-
[tex]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[/tex]
