Question

In a school sports day, there are 110 students taking part in 3 events i.e. athletic, netball, and soccer. Some of them are also supporters. Overall 43 of them are girls. 40 students take part in athletic. There are 25 girls taking part in netball, and 5 play netball and athletic. As for boys, only 30 boys play soccer, and only 15 take part in athletic. Meanwhile, 20 students act as supporters. The number of boys who play soccer only is 6 times more than girls who take part in netball and athletic. Note that the events only girls play netball and only boys play soccer are mutually exclusive.

a. Illustrate the events. Write the proper symbol for each event.

b. If one student is selected, find the probability of:

i. student who play soccer and an athletic. (1 mark)

ii. student who play netball but not an athletic.
(1 mark)

iii. student who only take part in athletic.  

iv. student who take part in netball given that she is not an athletic, or the student play soccer.     

Answer 1

Solution

(a)

Total students = 110

girls = 43, boys = 67

athlete student = 40

girls and netball = 25

girls, netball and athlete = 5

boys soccer = 30

boys athlete =15

student supporters = 20

boys only play soccer = 6*5 =30

g -> girls ; b->boys ; a->athlete; n-> netball; s-> soccer; su-> supporters

(b)

(1)

P(sa) = 0

(as the boys plyaing soccer only play soccer)

(2)

students who play netball = 25

student who play both netball and athletic = 5

student inly play netnall = 20

hence P(n)-p(na) = 20/110

(3)

total boys taking part in athlete = 15

total girls taking part in athlete = 40-15 =25

girls in athlete and netball = 5

total girls taking part only in athlete = 25-5 =20

p(student only taking part in athlete) = (20+15)/110 = 35/110

(4)

P(n/not athlete) = P(nnot athlete)/P(not athlete)

P(nnot athlete) = 20/110 (from 2nd part)

total boys playing athlete = 15

total girls playing athlete = 25

hence total students not playing athlete = 110-25-15 = 70

P(non athlete) = 70/110

P(n/not athlete) = 20/70