The odds in favour of Team A winning its match are 2 : 3, and the odds in favour of Team B winning its match are 1 : 4. The two matches are independent. What is the probability that both teams win?

Odds in favour of 2 : 3 mean 2 favourable parts against 3 unfavourable, so P(A wins) = 2/(2 + 3) = 2/5; likewise P(B wins) = 1/(1 + 4) = 1/5. The matches are independent, so P(both win) = (2/5)(1/5) = 2/25. Reading '1 : 4' straight off as the probability 1/4 gives (2/5)(1/4) = 1/10 — odds compare the two parts with each other, while a probability compares one part with the whole. The value 3/25 = (3/5)(1/5) is the probability that A loses while B wins, and 3/20 combines both slips at once.