Question

Below, the two-way table is given for aclass of students.FreshmenSophomoreJuniorsSeniorsTotal62463Male 42Female 3TotalIf 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

Given the table, we want to calculate the probability of choosing a female student, given that it is a junior. Since we are conditioned that the student is a junior, we can forget all the table data excep for the column that says "junior"

For this column, we have that 2 students are male and 6 are female. That is, we have a total of 8 students.

Now, we want to calculate the probability. To do so, we simply divide the total number of possibilites such that the event "choosing a female" is true by the total number of people.

Since we have 6 female students, we have 6 possibilites of choosing a female. So the probability would be

`(6)/(8)=(2\cdot3)/(2\cdot4)=(3)/(4)=0.75`

To express it as a percentage, we simply multiply it by 100. So we get

`0.75\cdot100=75`