Question 307042
With a statement like "odds against" the first number is the number of occurrences of failure while the second is the number of occurrences of success. For example, if a horse has the odds of 3 to 2 against it, then 3 times it will lose while 2 times it will win. This is all out of 5 cases. So this means that the probability of winning is {{{2/(3+2)=2/5}}}



So in general, if the success of an event has the odds against it of m:n, then the probability of success is {{{n/(m+n)}}}



In this case, the odds against passing are 10 to 7, which means that the chances of passing the test is {{{7/(10+7)=7/17=0.411764706}}} which is about a 41.176% chance.