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.
The odds against red means the same as the odds for black. There are 7 black beans out of 11 so 7/11.
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
To determine the odds against an event happening, we need to find the number of unfavorable outcomes and divide it by the number of favorable outcomes.
In this case, the event is selecting a red bean. We have a total of 4 red beans and 7 black beans, so the number of unfavorable outcomes (selecting a black bean) is 7.
The number of favorable outcomes (selecting a red bean) is 4.
Therefore, the odds against the bean being red is 7 to 4.
To simplify this ratio, we can divide both the numerator and the denominator by the greatest common divisor (GCD) of 7 and 4, which is 1.
So, the simplified odds against the bean being red is 7/4.