Question

Four red and seven black beans are placed into a bag. If one of the beans is selected at random, determine the odds against the bean being red.

Answer 1

The odds against red means the same as the odds for black. There are 7 black beans out of 11 so 7/11.

Answer 2

I will have to disagree with Jen.

The odds in favour of some event is defined as
prob(that event) : prob(not that event)

since prob(red) = 4/11
then prob(not red) = 7/11

so odds against red = (7/11) : (4/11)
= 7 : 4