Six students who share a house all speak exactly two languages. Helga speaks only English and German; Ina speaks only German and Spanish; Jean-Pierre speaks only French and Spanish; Karim speaks only German and French; Lionel speaks only French and English whilst Mary speaks only Spanish and English.
If two of the students are chosen at random, what is the probability they speak a common language?
Select one option, then click Submit.
\frac{1}{2}
\frac{2}{3}
\frac{3}{4}
\frac{4}{5}
\frac{5}{6}
Select an option, then submit.
Sign in or create an account to reveal answers, view the solution, and save your progress. Create a free account to unlock practice and keep track of your work.
Senior Mathematical Challenge 2012 (2012)
One puzzle per day. Cryptarithm, Magic Square, Summit. No sign-up required to play.
Play daily puzzle →Interactive problems and curated lessons—water pouring, magic squares, knight's tour, and more.
Browse library →See how you rank. Top solvers by problems solved correctly. Sign in to climb the ranks.
View leaderboard →Senior Mathematical Challenge 2012 (2012)