Answer:
(a) check explanation
(b) The favourite topic among the students is Number, having a total sum of 60 students who chose the topic.
(c) the fraction of girls who chose statistics as their favourite is ¹/₈
(d) the fraction of boys who chose geometry as their favourite is ¹/₆
(e) the fraction of students who chose statistics that were boys is ²/₃
Step-by-step explanation:
From the given statement;
Total number of boys = 60
Total number of girls = 80
Total number of students who chose Number = 60, number of boys = 20, number of girls = 40
Total number of students who chose Algebra = 30, number of boys = ?, number of girls = ?
Total number of students who chose geometry = 20, number of boys = 10, number of girls = 10
number of boys who chose statistics = 20, number of girls = ?
let the number of boys who chose algebra = x
20 boys(number) + x boys(algebra) + 10 boys (geometry) + 20 boys (statistics) = 60
50 + x = 60
x = 60 - 50
x = 10 boys
Thus, 10 boys chose algebra, then (30 - 10) girls chose algebra, i.e 20 girls.
Let the number of girls who chose statistics = y
40 girls(number) + 20 girls(algebra) + 10 girls(geometry) + y girls (statistics) = 80
70 + y = 80
y = 80 - 70
y = 10 girls
Thus, 10 girls chose statistics
Now complete the two-way table as follows;
(a) Two-way table
Boys Girls Total
Algebra 10 20 30
Geometry 10 10 20
Number 20 40 60
Statistics 20 10 30
Total 60 80 140
(b) The favourite topic among the students is Number, having a total sum of 60 students who chose the topic.
(c) the fraction of girls who chose statistics as their favourite;
[tex]= \frac{number \ of \ girls \ who \ chose \ statistics }{Total \ number \ of \ girls} \\\\= \frac{10}{80} \\\\= \frac{1}{8}[/tex]
(d) the fraction of boys who chose geometry as their favourite;
[tex]= \frac{number \ of \ boys \ who \ chose \ geometry }{Total \ number \ of \ boys} \\\\= \frac{10}{60} \\\\= \frac{1}{6}[/tex]
(e) the fraction of students who chose statistics that were boys is calculated as;
[tex]= \frac{number \ of \ boys \ who \ chose \ statistics }{Total \ number \ of \ students \ who \ chose \ statistics} \\\\= \frac{20}{30} \\\\= \frac{2}{3}[/tex]
