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Australian AMC 2019 - Intermediate Question 14

AMC AUSTRALIA · Australian AMC 2019 - Intermediate

Question 14

In a year 10 Maths class, there are 30 students. Each student is either 15 or 16 years old, and either left- or right-handed.
The ratio of right-handed students to left-handed students is 4 : 1, the ratio of 15 year olds to 16 year olds is 1 : 2 and the ratio of left-handed 15 year olds to left-handed 16 year olds is 1 : 5.
If the names of the students in this class are placed in a hat and one is selected at random, what is the probability that the student selected is 15 years old and right-handed?
  1. $\frac1{30}$
  2. $\frac16$
  3. $\frac3{10}$
  4. $\frac12$
  5. $\frac45$