The ‘odds’ in favour of an event A are quoted as ‘a to b’ if and only if P(A) = a/(a + b). The ‘odds against’ are then ‘b to a’ (which is the usual way to quote odds in betting situations).

(a) If an insurance company quotes odds of 3 to 1 in favour of an individual 70 years of age surviving another ten years, what is the corresponding probability?

(b) If the probability of a successful transplant operation is 1/8 , what are the odds against success?