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 ?
2. What proportion of good students are male ?
3. What proportion of female students are good ?
4. How many students are both male and good ?
5.Among average students, what is the ratio of male to female ?
(a) 1: 2
(b) 2 : 1
(c) 3 : 2
(d) 2 : 3
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)
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