A recruitment blog reports that the odds AGAINST a particular candidate being selected are 7 : 4. What is the probability that the candidate IS selected?

Odds against an event compare the ways it can fail to the ways it can happen, so failure : success = 7 : 4. Those 11 parts make up the whole, and selection takes 4 of them: 4/(7 + 4) = 4/11. Trap 7/11 reads the ratio as odds IN FAVOUR and so reports the chance of rejection. Trap 4/7 divides by the failure count 7 instead of by the total of 11 parts — odds are a ratio of two parts, not a fraction of the whole. Trap 1/2 ignores the stated odds altogether.