Question

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Answer 1

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;

$= \frac{number \ of \ girls \ who \ chose \ statistics }{Total \ number \ of \ girls} \\\\= \frac{10}{80} \\\\= \frac{1}{8}$

(d) the fraction of boys who chose geometry as their favourite;

$= \frac{number \ of \ boys \ who \ chose \ geometry }{Total \ number \ of \ boys} \\\\= \frac{10}{60} \\\\= \frac{1}{6}$

(e) the fraction of students who chose statistics that were boys is calculated as;

$= \frac{number \ of \ boys \ who \ chose \ statistics }{Total \ number \ of \ students \ who \ chose \ statistics} \\\\= \frac{20}{30} \\\\= \frac{2}{3}$