Respuesta :
[tex]\text{probability}=\frac{\text{ number of favorable cases}}{\text{ total number of }cases}[/tex]
Total number of students = 4 + 6 + 2 + 2 + 3 + 4 + 6 + 3 = 30
The probability that a student is female given that it is a junior is computed as follows:
[tex]\text{ P(}female|junior\text{)=}\frac{P(female\cap junior)}{P(junior)}[/tex]The probability that a student is female and junior is:
[tex]P(female\cap junior)=\frac{6}{30}=\frac{1}{5}[/tex]The probability that a student is a junior is:
[tex]P(junior)=\frac{2+6}{30}=\frac{8}{30}=\frac{4}{15}[/tex]Finally, The probability that a student is female given that it is a junior is:
[tex]P(female|junior)=\frac{\frac{1}{5}}{\frac{4}{15}}=\frac{1}{5}\cdot\frac{15}{4}=\frac{3}{4}=0.75\text{ or 75\%}[/tex]