Question

usBelow, the two-way table is given for aclass of students.FreshmenSophomoreJuniorsSeniorsTotalMale4622Female3463TotalIf a student is selected at random, find theprobability the student is a female given that it'sa junior. Round to the nearest whole percent.[?]%

Answer 1

`\text{probability}=\frac{\text{ number of favorable cases}}{\text{ total number of }cases}`

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:

`\text{ P(}female|junior\text{)=}(P(female\cap junior))/(P(junior))`

The probability that a student is female and junior is:

`P(female\cap junior)=(6)/(30)=(1)/(5)`

The probability that a student is a junior is:

`P(junior)=(2+6)/(30)=(8)/(30)=(4)/(15)`

Finally, The probability that a student is female given that it is a junior is:

`P(female|junior)=((1)/(5))/((4)/(15))=(1)/(5)\cdot(15)/(4)=(3)/(4)=0.75\text{ or 75\%}`