Problem 29 · 2018 Math Kangaroo
Stretch
Counting & Probability
proportioncareful-counting
In a class there are 40% more girls than boys. The probability that a student representative team of two students randomly selected from this class is made up of exactly one girl and one boy is exactly \(\tfrac{1}{2}\). How many children are there in this class?
Show answer
Answer: C — 36
Show hints
Hint 1 of 2
Let the number of boys be b; girls are 1.4b, and 1.4b must be a whole number.
Still stuck? Show hint 2 →
Hint 2 of 2
Write the probability of one girl + one boy and set it to 1/2.
Show solution
Approach: set up the mixed-pair probability and solve
- Let boys = b and girls = 1.4b, so the class has 2.4b children.
- Set P(one girl and one boy) = (girls·boys)/C(total,2) equal to 1/2 and look for a whole-number class.
- A class of 36 (15 boys and 21 girls) gives 15·21 / C(36,2) = 315/630 = 1/2.
- Answer: 36.
Mark:
· log in to save