🦘 Math Kangaroo Grade All Felix 1-2 Ecolier 3-4 Benjamin 5-6 Kadett 7-8 Junior 9-10 Student 11-12 ⇄ switch contest
2017 Math Kangaroo

Problem 9

Problem 9 · 2017 Math Kangaroo Medium
Counting & Probability careful-counting

In each of the five boxes (A) to (E) there are red and blue balls. Benedict wants to take exactly one ball, without looking, out of one of these boxes, and hopes to get a blue ball. In which box is the probability of that happening greatest?

Show answer
Answer: B — 6 blue, 4 red
Show hints
Hint 1 of 2
For each box the chance of a blue ball is blues divided by total balls.
Still stuck? Show hint 2 →
Hint 2 of 2
Compare the five fractions and pick the largest.
Show solution
Approach: compare the blue fractions
  1. The chances are 10/18, 6/10, 8/14, 7/14, 12/21.
  2. As decimals: 0.56, 0.60, 0.57, 0.50, 0.57.
  3. The greatest is 6/10 = 0.60, which is box B.
Mark: · log in to save