The following distribution table represents preferences for two types of cereals by 2000 boys and girls. Determine the probability that the person is a boy, given that the person likes Fruity Cereal.

Question

The following distribution table represents preferences for two types of cereals by 2000 boys and girls.  Determine the probability that the person is a boy, given that the person likes Fruity Cereal.

Quizplus · Accepted Answer

We need to find the probability of a person being a boy given that they like Fruity Cereal. We can use Bayes' theorem:

P(Boy | Fruity) = P(Fruity | Boy) * P(Boy) / P(Fruity)

P(Fruity) can be found by summing the number of people who like Fruity Cereal, regardless of gender:

P(Fruity) = (500 + 700) / 2000 = 1.2/2 = 0.6

P(Fruity | Boy) is the proportion of boys who like Fruity Cereal:

P(Fruity | Boy) = 500/1000 = 0.5

P(Boy) is the proportion of boys in the sample:

P(Boy) = 1000 / 2000 = 0.5

Now we can substitute these values into Bayes' theorem:

P(Boy | Fruity) = 0.5 * 0.5 / 0.6 = 0.4166

So the probability that the person is a boy, given that they like Fruity Cereal, is approximately 0.4166 or 500/1200. Therefore, the best choice is D, 500/1,200.

The Following Distribution Table Represents Preferences for Two Types of Cereals