Question

Anyone can answer this fully correctly ll of them ? really need help
2. In a secondary school, there are 400 male students and 600 female students. 50% of the male students and 55% of the female students are in senior secondary curriculum, the others are in junior secondary curriculum. The school had appointed 8% of senior male students and 10% of senior female students to be the student leaders. No junior secondary student can be student leader.

(a) If a student is selected at random in the school, find the probability that (i) the student is a senior student.





(II) the student is a female student leader.






(b) Suppose a student is selected and known to be NOT a student leader, what is the probability that (i) the student is a male student.






(ii) the student is a senior female student.

Answer 1

Given :

No of male students = 400

No of female students = 600

% of male students who are in  senior secondary curriculum= 50 %

% of female students who are in  senior secondary curriculum= 55 %

% of senior male students  appointed as student leaders = 8 %

% of senior female students  appointed as student leaders = 10 %

To Find :

(a) If a student is selected at random in the school then  find the probability that :

(|) the selected  student is a senior student

(||) the selected student is a female student leader

(b) If a student is selected and known to be NOT a student leader then find  is the probability that:

(|) the  selected student is a male student

(||) the selected student is a senior female student

Solution :

The no of male students in senior secondary is :

= 50 % of total no of male students

= 50 % of 400

$= \frac{50}{100}\times 400$

= 200

The no of female students in senior secondary is :

= 55 % of total no of female students

= 55 % of 600

= $\frac{55}{100} \times 600$

= 330

So, total no of students in senior secondary = 200 + 330 = 530

Now no senior male students who are leader:

= 8 % of senior male students

= 16 students

And  no senior female students who are leader:

= 10 % of senior female students

= 33 students

Now on random selection of a student in school :

(i)  Probability that its a senior student = $\frac{Total \hspace2 no \hspace2 of \hspace2 senior \hspace2 students }{Total \hspace2 no \hspace2 of \hspace2 students }$

                                                          $= \frac{530}{1000}$

                                                          $= \frac{53}{100}$

(ii) Probability that its a female student leader =$\frac{no \hspace2 of \hspace2 female \hspace2 student \hspace2 leaders }{Total \hspace2 no \hspace2 of \hspace2 students }$

                                                                            $= \frac{33}{1000}$

Now when it is known that selected student is not a leader , then :

(i) Probability that its a male student = $\frac{no \hspace2 of \hspace2 male \hspace2 students }{no \hspace2 of \hspace2 students \hspace2 who \hspace2 are \hspace2 not \hspace2 leaders }$

                                                            $= \frac{400}{1000- (16 + 33)} = \frac{400}{1000-49} = \frac{400}{951}$

(ii) Probability that its a senior female student = $\frac{Total \hspace2 no \hspace2 senior \hspace2 female \hspace2 students }{Total \hspace2 no \hspace2 of \hspace2 students }$

                                                                          =$\frac{330}{1000} = \frac{33}{100}$

So, the answers are :

a).

(i) = $\frac{53}{100}$

(ii)=$\frac{33}{1000}$

b).

(i) =$\frac{400}{951}$

(ii)=$\frac{33}{100}$