The probability that a student passes a test is 0.7. What are the odds AGAINST the student passing?

P(fail) = 1 − 0.7 = 0.3. Odds against an event compare the unfavourable part with the favourable part, so the odds against passing are 0.3 : 0.7 = 3 : 7. The reversed ratio 7 : 3 gives the odds IN FAVOUR, while 7 : 10 is just the probability written as a ratio.