### Directions

A professor Keeps data on students tabulated by performance and sex of the student .The data are kept on a computer disk but, unfortunately; some of them are lost because of a virus. Only the following could be recovered :

Panic buttons were pressed but of no avail. An expert committee was formed , which decided that the following facts were self-evident:

(a) Half the students were either excellent or good

(b) 40% of the students were females

(c) One third of the male students were average

**1. How many students are both female and excellent ?**

(a) 0

(b) 8

(c) 16

(d) 32

**2. What proportion of good students are male ?**

(a) 0

(b) 0.73

(c) 0.4

(d) 1.0

**3. What proportion of female students are good ?**

(a) 0

(b) 0.25

(c) 0.5

(d) 1.0

**4. How many students are both male and good ?**

(a) 10

(b) 16

(c) 22

(d) 48

**5.Among average students, what is the ratio of male to female ?**

(a) 1: 2

(b) 2 : 1

(c) 3 : 2

(d) 2 : 3

### Solutions:

1__5 : First complete the table with the help of the facts provided as shown below :

No. of females = 32

But 40% of the students were females.

. . Total no. of students = ( 100/40x32)

= 80

No.of male students = ( 80-32) = 48

. . No of male students who were average

= (1/3x 48) = 16

1 : No. of students who are both female and excellent = none.

2. Proportion of good students who are male

= 22/30 = 11/15 = 0.73

3. Proportion of female students who are good

= 8/32= 1/4 = 0.25

4. No. of students who are both male and good = 22.

5. Among average students, the ratio of male to female = 16 : 24 = 2: 3

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